We investigate some new subclasses of analytic functions of Janowski type of complex order.We also study inclusion properties,distortion theorems,coefficient bounds and radius of convexity of the functions.Moreover,an...We investigate some new subclasses of analytic functions of Janowski type of complex order.We also study inclusion properties,distortion theorems,coefficient bounds and radius of convexity of the functions.Moreover,analytic properties of these classes under certain integral operator are also discussed.Our findings are more comprehensive than the existing results in the literature.展开更多
In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fracti...In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fractional calculus.Specially,the order is defined as an iterative function that incorporates the current state of the system.By analyzing phase diagrams,time sequences,bifurcations,Lyapunov exponents and fuzzy entropy complexity,the dynamics of the proposed map are investigated comparing with the constant-order fractional sine map.The results reveal that the variable order has a good effect on improving the chaotic performance,and it enlarges the range of available parameter values as well as reduces non-chaotic windows.Multiple coexisting attractors also enrich the dynamics of VFSM and prove its sensitivity to initial values.Moreover,the sequence generated by the proposed map passes the statistical test for pseudorandom number and shows strong robustness to parameter estimation,which proves the potential applications in the field of information security.展开更多
Based on the stability theory of the linear fractional order system, projective synchronization of a complex network is studied in the paper, and the coupling functions of the connected nodes are identified. With this...Based on the stability theory of the linear fractional order system, projective synchronization of a complex network is studied in the paper, and the coupling functions of the connected nodes are identified. With this method, the projective synchronization of the network with different fractional order chaos nodes can be achieved, besides, the number of the nodes does not affect the stability of the whole network. In the numerical simulations, the chaotic fractional order Lu system, Liu system and Coullet system are chosen as examples to show the effectiveness of the scheme.展开更多
A theory of a class of higher order singular integral under the operator (L f) (u) =[u1 σf/σu1(u) - u1σf/σu1(u) + f(u)] is given. We transform the higher order singular integral to a usual Cauchy integr...A theory of a class of higher order singular integral under the operator (L f) (u) =[u1 σf/σu1(u) - u1σf/σu1(u) + f(u)] is given. We transform the higher order singular integral to a usual Cauchy integral, extend the permutation formula of the higher order singular integral deduced by Qian and Zhong in [4] to a general case, and discuss the regularization problem of the higher order singular integral equations with Cauchy kernel and variable coefficients on complex hypersphere.展开更多
Highly ordered mesoporous NiMoO4 material was successfully synthesized using mesoporous silica KIT-6 as hard template via vacuum nanocasting method. The structure was characterized by means of XRD, TEM, N2 adsorption-...Highly ordered mesoporous NiMoO4 material was successfully synthesized using mesoporous silica KIT-6 as hard template via vacuum nanocasting method. The structure was characterized by means of XRD, TEM, N2 adsorption-desorption, Raman and FT-IR. The mesoporous NiMoO4 with the coexistence of a-NiMoO4 and fl-NiMoO4 showed well-ordered mesoporous structure, a bimodal pore size distribution and crystalline framework. The catalytic performance of NiMoOa was investigated for oxidative dehydrogenation of propane. It is demonstrated that the mesoporous NiMoO4 catalyst with more surface active oxygen species showed better catalytic performance in oxidative dehydrogena- tion of propane in comparison with bulk NiMoO4.展开更多
Several approximate methods have been used to find approximate solutions of elliptic systems of first order equations. One common method is the Newton imbedding approach, i.e. the parameter extension method. In this a...Several approximate methods have been used to find approximate solutions of elliptic systems of first order equations. One common method is the Newton imbedding approach, i.e. the parameter extension method. In this article, we discuss approximate solutions to discontinuous Riemann-Hilbert boundary value problems, which have various applications in mechanics and physics. We first formulate the discontinuous Riemann-Hilbert problem for elliptic systems of first order complex equations in multiply connected domains and its modified well-posedness, then use the parameter extensional method to find approximate solutions to the modified boundary value problem for elliptic complex systems of first order equations, and then provide the error estimate of approximate solutions for the discontinuous boundary value problem.展开更多
In the paper, we study a high order numerical boundary scheme for solving the complex moving boundary problem on a fixed Cartesian mesh, and numerically investigate the moving rigid body with the complex boundary unde...In the paper, we study a high order numerical boundary scheme for solving the complex moving boundary problem on a fixed Cartesian mesh, and numerically investigate the moving rigid body with the complex boundary under the impingement of an inviscid shock wave. Based on the high order inverse Lax-Wendroff(ILW) procedure developed in the previous work(TAN, S. and SHU, C. W. A high order moving boundary treatment for compressible inviscid flows. Journal of Computational Physics, 230(15),6023–6036(2011)), in which the authors only considered the translation of the rigid body,we consider both translation and rotation of the body in this paper. In particular, we reformulate the material derivative on the moving boundary with no-penetration condition, and the newly obtained formula plays a key role in the proposed algorithm. Several numerical examples, including cylinder, elliptic cylinder, and NACA0012 airfoil, are given to indicate the effectiveness and robustness of the present method.展开更多
Outer synchronization between two different fractional-order general complex dynamical networks is investigated in this paper. Based on the stability theory of the fractional-order system, the sufficient criteria for ...Outer synchronization between two different fractional-order general complex dynamical networks is investigated in this paper. Based on the stability theory of the fractional-order system, the sufficient criteria for outer synchronization are derived analytically by applying the nonlinear control and the bidirectional coupling methods. The proposed synchronization method is applicable to almost all kinds of coupled fractional-order general complex dynamical networks. Neither a symmetric nor irreducible coupling configuration matrix is required. In addition, no constraint is imposed on the inner-coupling matrix. Numerical examples are also provided to demonstrate the validity of the presented synchronization scheme. Numeric evidence shows that both the feedback strength k and the fractional order a can be chosen appropriately to adjust the synchronization effect effectively.展开更多
This paper focuses on synchronization of fractionalorder complex dynamical networks with decentralized adaptive coupling.Based on local information among neighboring nodes,two fractional-order decentralized adaptive s...This paper focuses on synchronization of fractionalorder complex dynamical networks with decentralized adaptive coupling.Based on local information among neighboring nodes,two fractional-order decentralized adaptive strategies are designed to tune all or only a small fraction of the coupling gains respectively.By constructing quadratic Lyapunov functions and utilizing fractional inequality techniques,Mittag-Leffler function,and Laplace transform,two sufficient conditions are derived for reaching network synchronization by using the proposed adaptive laws.Finally,two numerical examples are given to verify the theoretical results.展开更多
In this paper, a new mechanism for the emergence of scale-free distribution is proposed. It is more realistic than the existing mechanism. Based on our mechanism, a model responsible for the scale-free distribution wi...In this paper, a new mechanism for the emergence of scale-free distribution is proposed. It is more realistic than the existing mechanism. Based on our mechanism, a model responsible for the scale-free distribution with an exponent in a range of 3-to-5 is given. Moreover, this model could also reproduce the exponential distribution that is discovered in some real networks. Finally, the analytical result of the model is given and the simulation shows the validity of our result,展开更多
This paper considers the Riemann-Hilbert problem for linear mixed(elliptichyperbolic) complex equations of first order with degenerate curve in a simply connected domain. We first give the representation theorem and...This paper considers the Riemann-Hilbert problem for linear mixed(elliptichyperbolic) complex equations of first order with degenerate curve in a simply connected domain. We first give the representation theorem and uniqueness of solutions for such boundary value problem. Then by using the methods of successive iteration and parameter extension, the existence of solutions for this problem is proved.展开更多
This paper investigates the synchronization problem of fractional-order complex networks with nonidentical nodes. The generalized projective synchronization criterion of fractional-order complex networks with order 0 ...This paper investigates the synchronization problem of fractional-order complex networks with nonidentical nodes. The generalized projective synchronization criterion of fractional-order complex networks with order 0 〈 q 〈 1 is obtained based on the stability theory of the fractional-order system. The control method which combines active control with pinning control is then suggested to obtain the controllers. Furthermore, the adaptive strategy is applied to tune the control gains and coupling strength. Corresponding numerical simulations are performed to verify and illustrate the theoretical results.展开更多
Multi-link networks are universal in the real world such as relationship networks,transportation networks,and communication networks.It is significant to investigate the synchronization of the network with multi-link....Multi-link networks are universal in the real world such as relationship networks,transportation networks,and communication networks.It is significant to investigate the synchronization of the network with multi-link.In this paper,considering the complex network with uncertain parameters,new adaptive controller and update laws are proposed to ensure that complex-valued multilink network realizes finite-time complex projective synchronization(FTCPS).In addition,based on fractional-order Lyapunov functional method and finite-time stability theory,the criteria of FTCPS are derived and synchronization time is given which is associated with fractional order and control parameters.Meanwhile,numerical example is given to verify the validity of proposed finite-time complex projection strategy and analyze the relationship between synchronization time and fractional order and control parameters.Finally,the network is applied to image encryption,and the security analysis is carried out to verify the correctness of this method.展开更多
UV-Vis spectrum and the third-order nonlinear optical properties of the chiral camphor-derived β-diketonate have been studied at the B3LYP/6-31G* level. The results showed that the introduction of electron-drawing g...UV-Vis spectrum and the third-order nonlinear optical properties of the chiral camphor-derived β-diketonate have been studied at the B3LYP/6-31G* level. The results showed that the introduction of electron-drawing group -CF3 and -C3F7 on β-diketonate made the strongest absorption peak red-shift and the lowest energy absorption blue-shied. Introduction of -OC2H5 on the benzene or pyridine ring made the lowest energy absorption blue-shift. When the -C2H3 was introduced on the benzene or pyridine ring, the lowest energy absorption was red-shifted. Introduction of electron-donating group on β-diketonate can enlarge their nonlinear optical properties. On the contrary, the introduction of electron-drawing group dropped it down.展开更多
The complex derivative D^α±jβ, with α, β ∈ R+ is a generalization of the concept of integer derivative, where α = 1,β = 0. Fractional-order electric elements and circuits are becoming more and more attrac...The complex derivative D^α±jβ, with α, β ∈ R+ is a generalization of the concept of integer derivative, where α = 1,β = 0. Fractional-order electric elements and circuits are becoming more and more attractive. In this paper, the complexorder electric elements concept is proposed for the first time, and the complex-order elements are modeled and analyzed.Some interesting phenomena are found that the real part of the order affects the phase of output signal, and the imaginary part affects the amplitude for both the complex-order capacitor and complex-order memristor. More interesting is that the complex-order capacitor can do well at the time of fitting electrochemistry impedance spectra. The complex-order memristor is also analyzed. The area inside the hysteresis loops increases with the increasing of the imaginary part of the order and decreases with the increasing of the real part. Some complex case of complex-order memristors hysteresis loops are analyzed at last, whose loop has touching points beyond the origin of the coordinate system.展开更多
This paper investigates the stability of the Francis hydro-turbine governing system with complex penstocks in the grid-connected mode. Firstly, a novel fractional-order nonlinear mathematical model of a Francis hydro-...This paper investigates the stability of the Francis hydro-turbine governing system with complex penstocks in the grid-connected mode. Firstly, a novel fractional-order nonlinear mathematical model of a Francis hydro-turbine governing system with complex penstocks is built from an engineering application perspective. This model is described by state-space equations and is composed of the Francis hydro-turbine model, the fractional-order complex penstocks model, the third-order generator model, and the hydraulic speed governing system model. Based on stability theory for a fractional-order nonlinear system, this study discovers a basic law of the bifurcation points of the above system with a change in the fractional-order a. Secondly, the stable region of the governing system is investigated in detail,and nonlinear dynamical behaviors of the system are identified and studied exhaustively via bifurcation diagrams, time waveforms, phase orbits, Poincare maps, power spectrums and spectrograms. Results of these numerical experiments provide a theoretical reference for further studies of the stability of hydropower stations.展开更多
In this paper, using Nevanlinna theory of the value distribution of meromorphic functions, the problem of growth order of solutions of a class of system of complex difference equations is investigated, some results ar...In this paper, using Nevanlinna theory of the value distribution of meromorphic functions, the problem of growth order of solutions of a class of system of complex difference equations is investigated, some results are improved and generalized. More precisely,some results of the growth order of solutions of system of differential equations to difference equations are extended.展开更多
A novel Schiff base ligand (HL) derived from S-methyldithiocabazate and pmethoxylbenzaldehyde was prepared and characterized. The Schiff base ligand acts as a single negatively charged bidentate ligand fondng D-M-D ty...A novel Schiff base ligand (HL) derived from S-methyldithiocabazate and pmethoxylbenzaldehyde was prepared and characterized. The Schiff base ligand acts as a single negatively charged bidentate ligand fondng D-M-D type comPlex (D=donor, M=metal). Single crystal X-ray diffraction analysis of the copper(Ⅱ) complex established that the geometry around Cu (Ⅱ) is square-planar with two equivalent M-N and M-S bonds. The two phenyl rings and the coordinated plane are almost in one plane fotheng an electronic delocalization system. Their thirdorder response was also studied.展开更多
文摘We investigate some new subclasses of analytic functions of Janowski type of complex order.We also study inclusion properties,distortion theorems,coefficient bounds and radius of convexity of the functions.Moreover,analytic properties of these classes under certain integral operator are also discussed.Our findings are more comprehensive than the existing results in the literature.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.62071496,61901530,and 62061008)the Natural Science Foundation of Hunan Province of China(Grant No.2020JJ5767).
文摘In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fractional calculus.Specially,the order is defined as an iterative function that incorporates the current state of the system.By analyzing phase diagrams,time sequences,bifurcations,Lyapunov exponents and fuzzy entropy complexity,the dynamics of the proposed map are investigated comparing with the constant-order fractional sine map.The results reveal that the variable order has a good effect on improving the chaotic performance,and it enlarges the range of available parameter values as well as reduces non-chaotic windows.Multiple coexisting attractors also enrich the dynamics of VFSM and prove its sensitivity to initial values.Moreover,the sequence generated by the proposed map passes the statistical test for pseudorandom number and shows strong robustness to parameter estimation,which proves the potential applications in the field of information security.
基金Project supported by the National Natural Science Foundation of China(Nos.60573172and60973152)the Superior University Doctor Subject Special Scientific Research Foundation of China(Grant No.20070141014)the Natural Science Foundation of Liaoning Province,China(Grant No.20082165)
文摘Based on the stability theory of the linear fractional order system, projective synchronization of a complex network is studied in the paper, and the coupling functions of the connected nodes are identified. With this method, the projective synchronization of the network with different fractional order chaos nodes can be achieved, besides, the number of the nodes does not affect the stability of the whole network. In the numerical simulations, the chaotic fractional order Lu system, Liu system and Coullet system are chosen as examples to show the effectiveness of the scheme.
基金supported by the Natural Science Foundation of Fujian Province of China(S0850029,2008J0206)Innovation Foundation of Xiamen University(XDKJCX20063019),the National Science Foundation of China (10771174)
文摘A theory of a class of higher order singular integral under the operator (L f) (u) =[u1 σf/σu1(u) - u1σf/σu1(u) + f(u)] is given. We transform the higher order singular integral to a usual Cauchy integral, extend the permutation formula of the higher order singular integral deduced by Qian and Zhong in [4] to a general case, and discuss the regularization problem of the higher order singular integral equations with Cauchy kernel and variable coefficients on complex hypersphere.
基金supported by NSFC(21073235,21173270,21177160,21376261)863 Program(2013AA065302)PetroChina Innovation Foundation(2011D-5006-0403)
文摘Highly ordered mesoporous NiMoO4 material was successfully synthesized using mesoporous silica KIT-6 as hard template via vacuum nanocasting method. The structure was characterized by means of XRD, TEM, N2 adsorption-desorption, Raman and FT-IR. The mesoporous NiMoO4 with the coexistence of a-NiMoO4 and fl-NiMoO4 showed well-ordered mesoporous structure, a bimodal pore size distribution and crystalline framework. The catalytic performance of NiMoOa was investigated for oxidative dehydrogenation of propane. It is demonstrated that the mesoporous NiMoO4 catalyst with more surface active oxygen species showed better catalytic performance in oxidative dehydrogena- tion of propane in comparison with bulk NiMoO4.
文摘Several approximate methods have been used to find approximate solutions of elliptic systems of first order equations. One common method is the Newton imbedding approach, i.e. the parameter extension method. In this article, we discuss approximate solutions to discontinuous Riemann-Hilbert boundary value problems, which have various applications in mechanics and physics. We first formulate the discontinuous Riemann-Hilbert problem for elliptic systems of first order complex equations in multiply connected domains and its modified well-posedness, then use the parameter extensional method to find approximate solutions to the modified boundary value problem for elliptic complex systems of first order equations, and then provide the error estimate of approximate solutions for the discontinuous boundary value problem.
基金Project supported by the National Natural Science Foundation of China (Nos. 11901555, 11901213,11871448, and 11732016)the National Numerical Windtunnel Project (No. NNW2019ZT4-B10)。
文摘In the paper, we study a high order numerical boundary scheme for solving the complex moving boundary problem on a fixed Cartesian mesh, and numerically investigate the moving rigid body with the complex boundary under the impingement of an inviscid shock wave. Based on the high order inverse Lax-Wendroff(ILW) procedure developed in the previous work(TAN, S. and SHU, C. W. A high order moving boundary treatment for compressible inviscid flows. Journal of Computational Physics, 230(15),6023–6036(2011)), in which the authors only considered the translation of the rigid body,we consider both translation and rotation of the body in this paper. In particular, we reformulate the material derivative on the moving boundary with no-penetration condition, and the newly obtained formula plays a key role in the proposed algorithm. Several numerical examples, including cylinder, elliptic cylinder, and NACA0012 airfoil, are given to indicate the effectiveness and robustness of the present method.
基金supported by the National Natural Science Foundation of China (Grant No. 60873133)the National High Technology Research and Development Program of China (Grant No. 2007AA01Z478)
文摘Outer synchronization between two different fractional-order general complex dynamical networks is investigated in this paper. Based on the stability theory of the fractional-order system, the sufficient criteria for outer synchronization are derived analytically by applying the nonlinear control and the bidirectional coupling methods. The proposed synchronization method is applicable to almost all kinds of coupled fractional-order general complex dynamical networks. Neither a symmetric nor irreducible coupling configuration matrix is required. In addition, no constraint is imposed on the inner-coupling matrix. Numerical examples are also provided to demonstrate the validity of the presented synchronization scheme. Numeric evidence shows that both the feedback strength k and the fractional order a can be chosen appropriately to adjust the synchronization effect effectively.
基金supported by the"Chunhui Plan"Cooperative Research for Ministry of Education(Z2016133)the Open Research Fund of Key Laboratory of Automobile Engineering(Xihua University)+3 种基金Sichuan Province(szjj2016-017)the National Natural Science Foundation of China(51177137)the Scientific Research Foundation of the Education Department of Sichuan Province(16ZB0163)the China Scholarship Council
文摘This paper focuses on synchronization of fractionalorder complex dynamical networks with decentralized adaptive coupling.Based on local information among neighboring nodes,two fractional-order decentralized adaptive strategies are designed to tune all or only a small fraction of the coupling gains respectively.By constructing quadratic Lyapunov functions and utilizing fractional inequality techniques,Mittag-Leffler function,and Laplace transform,two sufficient conditions are derived for reaching network synchronization by using the proposed adaptive laws.Finally,two numerical examples are given to verify the theoretical results.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 60374037 and 60574036), the Program for New Century Excellent Talents of High Education of China(Grant No NCET 2005-290), The Special Research Fund for the Doctoral Program of High Education of China (Grant No 20050055013).Acknowledgments The authors would like to thank Réka Albert for useful discussion and are grateful to the anonymous referees for their valuable suggestions and comments, which have made this paper improved.
文摘In this paper, a new mechanism for the emergence of scale-free distribution is proposed. It is more realistic than the existing mechanism. Based on our mechanism, a model responsible for the scale-free distribution with an exponent in a range of 3-to-5 is given. Moreover, this model could also reproduce the exponential distribution that is discovered in some real networks. Finally, the analytical result of the model is given and the simulation shows the validity of our result,
基金Supported by the Natural Science Foundation of Guangdong Province(04010474) Supported by the Foundation of the Education Department of Anhui Province for Outstanding Young Teachers in University(2011SQRL172)
基金Supported by the National Natural Science Foundation of China (10971224)
文摘This paper considers the Riemann-Hilbert problem for linear mixed(elliptichyperbolic) complex equations of first order with degenerate curve in a simply connected domain. We first give the representation theorem and uniqueness of solutions for such boundary value problem. Then by using the methods of successive iteration and parameter extension, the existence of solutions for this problem is proved.
文摘This paper investigates the synchronization problem of fractional-order complex networks with nonidentical nodes. The generalized projective synchronization criterion of fractional-order complex networks with order 0 〈 q 〈 1 is obtained based on the stability theory of the fractional-order system. The control method which combines active control with pinning control is then suggested to obtain the controllers. Furthermore, the adaptive strategy is applied to tune the control gains and coupling strength. Corresponding numerical simulations are performed to verify and illustrate the theoretical results.
文摘Multi-link networks are universal in the real world such as relationship networks,transportation networks,and communication networks.It is significant to investigate the synchronization of the network with multi-link.In this paper,considering the complex network with uncertain parameters,new adaptive controller and update laws are proposed to ensure that complex-valued multilink network realizes finite-time complex projective synchronization(FTCPS).In addition,based on fractional-order Lyapunov functional method and finite-time stability theory,the criteria of FTCPS are derived and synchronization time is given which is associated with fractional order and control parameters.Meanwhile,numerical example is given to verify the validity of proposed finite-time complex projection strategy and analyze the relationship between synchronization time and fractional order and control parameters.Finally,the network is applied to image encryption,and the security analysis is carried out to verify the correctness of this method.
基金supported by the National Natural Science Foundation of China(21172161)
文摘UV-Vis spectrum and the third-order nonlinear optical properties of the chiral camphor-derived β-diketonate have been studied at the B3LYP/6-31G* level. The results showed that the introduction of electron-drawing group -CF3 and -C3F7 on β-diketonate made the strongest absorption peak red-shift and the lowest energy absorption blue-shied. Introduction of -OC2H5 on the benzene or pyridine ring made the lowest energy absorption blue-shift. When the -C2H3 was introduced on the benzene or pyridine ring, the lowest energy absorption was red-shifted. Introduction of electron-donating group on β-diketonate can enlarge their nonlinear optical properties. On the contrary, the introduction of electron-drawing group dropped it down.
文摘The complex derivative D^α±jβ, with α, β ∈ R+ is a generalization of the concept of integer derivative, where α = 1,β = 0. Fractional-order electric elements and circuits are becoming more and more attractive. In this paper, the complexorder electric elements concept is proposed for the first time, and the complex-order elements are modeled and analyzed.Some interesting phenomena are found that the real part of the order affects the phase of output signal, and the imaginary part affects the amplitude for both the complex-order capacitor and complex-order memristor. More interesting is that the complex-order capacitor can do well at the time of fitting electrochemistry impedance spectra. The complex-order memristor is also analyzed. The area inside the hysteresis loops increases with the increasing of the imaginary part of the order and decreases with the increasing of the real part. Some complex case of complex-order memristors hysteresis loops are analyzed at last, whose loop has touching points beyond the origin of the coordinate system.
基金supported by the Scientific Research Foundation of the National Natural Science Foundation-Outstanding Youth Foundation(No.51622906)National Natural Science Foundation of China (No.51479173)+4 种基金Fundamental Research Funds for the Central Universities (201304030577)Scientific Research Funds of Northwest A&F University (2013BSJJ095)the Scientific Research Foundation for Water Engineering in Shaanxi Province (2013slkj-12)the Science Fund for Excellent Young Scholars from Northwest A&F University (Z109021515)the Shaanxi Nova Program (2016KJXX-55)
文摘This paper investigates the stability of the Francis hydro-turbine governing system with complex penstocks in the grid-connected mode. Firstly, a novel fractional-order nonlinear mathematical model of a Francis hydro-turbine governing system with complex penstocks is built from an engineering application perspective. This model is described by state-space equations and is composed of the Francis hydro-turbine model, the fractional-order complex penstocks model, the third-order generator model, and the hydraulic speed governing system model. Based on stability theory for a fractional-order nonlinear system, this study discovers a basic law of the bifurcation points of the above system with a change in the fractional-order a. Secondly, the stable region of the governing system is investigated in detail,and nonlinear dynamical behaviors of the system are identified and studied exhaustively via bifurcation diagrams, time waveforms, phase orbits, Poincare maps, power spectrums and spectrograms. Results of these numerical experiments provide a theoretical reference for further studies of the stability of hydropower stations.
基金Project Supported by the fundamental research funds for the Central Universities project of China(No.11614801)Combining with the project of Guangdong Province production(No.2011A090200044)
文摘In this paper, using Nevanlinna theory of the value distribution of meromorphic functions, the problem of growth order of solutions of a class of system of complex difference equations is investigated, some results are improved and generalized. More precisely,some results of the growth order of solutions of system of differential equations to difference equations are extended.
文摘A novel Schiff base ligand (HL) derived from S-methyldithiocabazate and pmethoxylbenzaldehyde was prepared and characterized. The Schiff base ligand acts as a single negatively charged bidentate ligand fondng D-M-D type comPlex (D=donor, M=metal). Single crystal X-ray diffraction analysis of the copper(Ⅱ) complex established that the geometry around Cu (Ⅱ) is square-planar with two equivalent M-N and M-S bonds. The two phenyl rings and the coordinated plane are almost in one plane fotheng an electronic delocalization system. Their thirdorder response was also studied.