Many systems can display a very short, rapid change stage (quasi-discontinuous region) inside a relatively very long and slow change process. A quantitative definition for the 'quasi-discontinuity' in these sy...Many systems can display a very short, rapid change stage (quasi-discontinuous region) inside a relatively very long and slow change process. A quantitative definition for the 'quasi-discontinuity' in these systems has been introduced. With the aid of a simplified model, some extraordinary Feigenbaum constants have been found inside the period-doubling cascades, the relationship between the values of the extraordinary Feigenbaum constants and the quasi-discontinuity of the system has also been reported. The phenomenon has been observed in Pikovsky circuit and Rose-Hindmash model.展开更多
Consider a four-dimensional system having a two-dimensional invariant surface. By analyzing the solutions of bifurcation equations, this paper studied the bifurcation phenomena of a k multiple closed orbit in the inva...Consider a four-dimensional system having a two-dimensional invariant surface. By analyzing the solutions of bifurcation equations, this paper studied the bifurcation phenomena of a k multiple closed orbit in the invariant surface. Sufficient conditions for the existence of periodic orbits generated by the k multiple closed orbit were given.展开更多
In mountain ecosystems,plants are sensitive to climate changes,and an entire range of species distribution can be observed in a small area.Therefore,mountains are of great interest for climate–growth relationship ana...In mountain ecosystems,plants are sensitive to climate changes,and an entire range of species distribution can be observed in a small area.Therefore,mountains are of great interest for climate–growth relationship analysis.In this study,the Siberian spruce’s(Picea obovata Ledeb.)radial growth and its climatic response were investigated in the Western Sayan Mountains,near the SayanoShushenskoe Reservoir.Sampling was performed at three sites along an elevational gradient:at the lower border of the species range,in the middle,and at the treeline.Divergence of growth trends between individual trees was observed at each site,with microsite landscape-soil conditions as the most probable driver of this phenomenon.Cluster analysis of individual tree-ring width series based on inter-serial correlation was carried out,resulting in two sub-set chronologies being developed for each site.These chronologies appear to have substantial differences in their climatic responses,mainly during the cold season.This response was not constant due to regional climatic change and the local influence of the nearby Sayano-Shushenskoe Reservoir.The main response of spruce to growing season conditions has a typical elevational pattern expected in mountains:impact of temperature shifts with elevation from positive to negative,and impact of precipitation shifts in the opposite direction.Chronologies of trees,growing under more severe micro-conditions,are very sensitive to temperature during September–April and to precipitation during October–December,and they record both inter-annual and long-term climatic variation.Consequently,it would be interesting to test if they indicate the Siberian High anticyclone,which is the main driver of these climatic factors.展开更多
This paper is concerned with the number and distributions of limit cycles of a cubic Z2-symmetry Hamiltonian system under quintic perturbation.By using qualitative analysis of differential equation,bifurcation theory ...This paper is concerned with the number and distributions of limit cycles of a cubic Z2-symmetry Hamiltonian system under quintic perturbation.By using qualitative analysis of differential equation,bifurcation theory of dynamical systems and the method of detection function,we obtain that this system exists at least 14 limit cycles with the distribution C91 [C11 ＋ 2（C32 2C12）].展开更多
A more recent branch of natural computing is DNA computing. At the theoretical level, DNA computing is powerful. This is due to the fact that DNA structure and processing suggest a series of new data structures and op...A more recent branch of natural computing is DNA computing. At the theoretical level, DNA computing is powerful. This is due to the fact that DNA structure and processing suggest a series of new data structures and operations, and to the fact of the massive parallelism. The insertion-deletion system （insdel system） is a DNA computing model based on two genetic operations： insertion and deletion which, working together, are very powerful, leading to characterizations of recursively enumerable lan- guages. When designing an insdel computer, it is natural to try to keep the underlying model as simple as possible. One idea is to use either only insertion operations or only deletion operations. By helping with a weak coding and a morphism, the family INS4^7DEL0^0 is equal to the family of recursively enumerable languages. It is an open problem proposed by Martin-Vide et al. on whether or not the parameters 4 and 7 appearing here can be replaced by smaller numbers. In this paper, our positive answer to this question is that INS2^4DEL0^0 can also play the same role as insertion and deletion. We suppose that the INS2^4DEL0^0 may be the least only-insertion insdel system in this situation. We will give some reasons supporting this conjecture in our paper.展开更多
This paper deals with a kind of fourth degree systems with perturbations. By using the method of multi-parameter perturbation theory and qualitative analysis, it is proved that the system can have six limit cycles.
We propose a novel approach called the robust fractional-order proportional-integral-derivative（FOPID）controller, to stabilize a perturbed nonlinear chaotic system on one of its unstable fixed points. The stability ...We propose a novel approach called the robust fractional-order proportional-integral-derivative（FOPID）controller, to stabilize a perturbed nonlinear chaotic system on one of its unstable fixed points. The stability analysis of the nonlinear chaotic system is made based on the proportional-integral-derivative actions using the bifurcation diagram. We extract an initial set of controller parameters, which are subsequently optimized using a quadratic criterion. The integral and derivative fractional orders are also identified by this quadratic criterion. By applying numerical simulations on two nonlinear systems, namely the multi-scroll Chen system and the Genesio-Tesi system,we show that the fractional PI~λD~μ controller provides the best closed-loop system performance in stabilizing the unstable fixed points, even in the presence of random perturbation.展开更多
In this paper, we propose and analyze a three-species predator prey system in the presence of additional food for top predator. It is assumed that the middle predator is acting as a prey as well as a predator and the ...In this paper, we propose and analyze a three-species predator prey system in the presence of additional food for top predator. It is assumed that the middle predator is acting as a prey as well as a predator and the top predator consumes both prey as well as middle predator. It is also considered that a constant amount of additional food for top predator exists in the ecosystem. The effects of harvesting of top predator are investigated. The existence and stability conditions of the equilibria have been discussed analytically. The Hopf bifurcation analysis of the system with respect to predation rate of prey to the top predator and the harvesting effort have been analyzed both analytically and numerically. Pontryagin＇s maximum principle is used to determine the optimal harvesting of top predator population to maximize the discounted net revenue. From our analysis, it is seen that the additional food has a significant impact to prevent the extinction risk of top predator population and also to increase revenue collection. Finally, some numerical results have been given in support of our analytical findings.展开更多
文摘Many systems can display a very short, rapid change stage (quasi-discontinuous region) inside a relatively very long and slow change process. A quantitative definition for the 'quasi-discontinuity' in these systems has been introduced. With the aid of a simplified model, some extraordinary Feigenbaum constants have been found inside the period-doubling cascades, the relationship between the values of the extraordinary Feigenbaum constants and the quasi-discontinuity of the system has also been reported. The phenomenon has been observed in Pikovsky circuit and Rose-Hindmash model.
文摘Consider a four-dimensional system having a two-dimensional invariant surface. By analyzing the solutions of bifurcation equations, this paper studied the bifurcation phenomena of a k multiple closed orbit in the invariant surface. Sufficient conditions for the existence of periodic orbits generated by the k multiple closed orbit were given.
基金funded by the Russian Foundation for Basic Research (project no.17-04-00315)
文摘In mountain ecosystems,plants are sensitive to climate changes,and an entire range of species distribution can be observed in a small area.Therefore,mountains are of great interest for climate–growth relationship analysis.In this study,the Siberian spruce’s(Picea obovata Ledeb.)radial growth and its climatic response were investigated in the Western Sayan Mountains,near the SayanoShushenskoe Reservoir.Sampling was performed at three sites along an elevational gradient:at the lower border of the species range,in the middle,and at the treeline.Divergence of growth trends between individual trees was observed at each site,with microsite landscape-soil conditions as the most probable driver of this phenomenon.Cluster analysis of individual tree-ring width series based on inter-serial correlation was carried out,resulting in two sub-set chronologies being developed for each site.These chronologies appear to have substantial differences in their climatic responses,mainly during the cold season.This response was not constant due to regional climatic change and the local influence of the nearby Sayano-Shushenskoe Reservoir.The main response of spruce to growing season conditions has a typical elevational pattern expected in mountains:impact of temperature shifts with elevation from positive to negative,and impact of precipitation shifts in the opposite direction.Chronologies of trees,growing under more severe micro-conditions,are very sensitive to temperature during September–April and to precipitation during October–December,and they record both inter-annual and long-term climatic variation.Consequently,it would be interesting to test if they indicate the Siberian High anticyclone,which is the main driver of these climatic factors.
基金Supported by the Natural Science Foundation of China（10802043 10826092） Acknowledgements We are grateful to Prof Li Ji-bin for his kind help and the referees＇ valuable suggestions.
文摘This paper is concerned with the number and distributions of limit cycles of a cubic Z2-symmetry Hamiltonian system under quintic perturbation.By using qualitative analysis of differential equation,bifurcation theory of dynamical systems and the method of detection function,we obtain that this system exists at least 14 limit cycles with the distribution C91 [C11 ＋ 2（C32 2C12）].
文摘A more recent branch of natural computing is DNA computing. At the theoretical level, DNA computing is powerful. This is due to the fact that DNA structure and processing suggest a series of new data structures and operations, and to the fact of the massive parallelism. The insertion-deletion system （insdel system） is a DNA computing model based on two genetic operations： insertion and deletion which, working together, are very powerful, leading to characterizations of recursively enumerable lan- guages. When designing an insdel computer, it is natural to try to keep the underlying model as simple as possible. One idea is to use either only insertion operations or only deletion operations. By helping with a weak coding and a morphism, the family INS4^7DEL0^0 is equal to the family of recursively enumerable languages. It is an open problem proposed by Martin-Vide et al. on whether or not the parameters 4 and 7 appearing here can be replaced by smaller numbers. In this paper, our positive answer to this question is that INS2^4DEL0^0 can also play the same role as insertion and deletion. We suppose that the INS2^4DEL0^0 may be the least only-insertion insdel system in this situation. We will give some reasons supporting this conjecture in our paper.
基金Project supported by the National Natural Science Foundation of China (No.10371072)the New Century Excellent Ttdents in University (No.NCBT-04-038)the Shanghai Leading Academic Discipline (No.T0401).
文摘This paper deals with a kind of fourth degree systems with perturbations. By using the method of multi-parameter perturbation theory and qualitative analysis, it is proved that the system can have six limit cycles.
基金Project supported by the Ministry of Higher Education and Scientific Research,Algeria(CNEPRU No.A10N01UN210120150002)
文摘We propose a novel approach called the robust fractional-order proportional-integral-derivative（FOPID）controller, to stabilize a perturbed nonlinear chaotic system on one of its unstable fixed points. The stability analysis of the nonlinear chaotic system is made based on the proportional-integral-derivative actions using the bifurcation diagram. We extract an initial set of controller parameters, which are subsequently optimized using a quadratic criterion. The integral and derivative fractional orders are also identified by this quadratic criterion. By applying numerical simulations on two nonlinear systems, namely the multi-scroll Chen system and the Genesio-Tesi system,we show that the fractional PI~λD~μ controller provides the best closed-loop system performance in stabilizing the unstable fixed points, even in the presence of random perturbation.
文摘In this paper, we propose and analyze a three-species predator prey system in the presence of additional food for top predator. It is assumed that the middle predator is acting as a prey as well as a predator and the top predator consumes both prey as well as middle predator. It is also considered that a constant amount of additional food for top predator exists in the ecosystem. The effects of harvesting of top predator are investigated. The existence and stability conditions of the equilibria have been discussed analytically. The Hopf bifurcation analysis of the system with respect to predation rate of prey to the top predator and the harvesting effort have been analyzed both analytically and numerically. Pontryagin＇s maximum principle is used to determine the optimal harvesting of top predator population to maximize the discounted net revenue. From our analysis, it is seen that the additional food has a significant impact to prevent the extinction risk of top predator population and also to increase revenue collection. Finally, some numerical results have been given in support of our analytical findings.
