Results on the existence of piecewise continuous solutions for two classes of initial value problems of impulsive singular fractional differential equations are obtained.
A delayed predator-prey model concerning impulsive spraying pesticides and releasing natural enemies is proposed and investigated,in which both the prey and the predator have a history that takes them through two stag...A delayed predator-prey model concerning impulsive spraying pesticides and releasing natural enemies is proposed and investigated,in which both the prey and the predator have a history that takes them through two stages:immature and mature.The global attractiveness of the pest-eradication periodic solution is discussed,and sufficient condition is obtained for the permanence of the system.Further,numerical simulations show that there is a characteristic sequence of bifurcations leading to a chaotic dynamics,which implies that the system with constant periodic impulsive perturbations admits rich and complex dynamics.展开更多
The existence of homoclinic solutions for the second-order p-Laplacian differential system( ρ( t) Φp( u'( t))) '-s( t) Φp( u( t))+ λf( t,u( t)) = 0 with impulsive effects Δ( ρ( tj) Φp( u'( tj))) = I...The existence of homoclinic solutions for the second-order p-Laplacian differential system( ρ( t) Φp( u'( t))) '-s( t) Φp( u( t))+ λf( t,u( t)) = 0 with impulsive effects Δ( ρ( tj) Φp( u'( tj))) = Ij( u( tj)) is studied. By using three critical points theorem and variational methods, the sufficient condition is established to guarantee that this p-Laplacian differential system with impulsive effects has at least one nontrivial homoclinic solution. Besides,an example is presented to illustrate the main result in the end of this paper.展开更多
We consider the impulsive effect on the exponential synchronization of neural networks with leakage delay under the sampled-data feedback control. We use an appropriate Lyapunov-Krasovskii functional combined with the...We consider the impulsive effect on the exponential synchronization of neural networks with leakage delay under the sampled-data feedback control. We use an appropriate Lyapunov-Krasovskii functional combined with the input delay approach and some inequality techniques to derive sufficient conditions that ensure the exponential synchronization of the delayed neural network. The conditions are formulated in terms of the leakage delay, the sampling period, and the exponential convergence rate. Numerical examples are given to demonstrate the usefulness and the effectiveness of the results.展开更多
Under internal blast loading,the response of a beam or plate is highly correlated with the phenomenon of saturated impulse,which governs the deflection of the structure.This paper aims to investigate the phenomenon of...Under internal blast loading,the response of a beam or plate is highly correlated with the phenomenon of saturated impulse,which governs the deflection of the structure.This paper aims to investigate the phenomenon of saturated impulse for fully clamped rectangular plates subjected to internal blast loading.Based on the rigid,perfectly plastic assumption,the relationship between saturation duration and saturation deflection is derived.Influences of the peak shock wave,the duration of shock wave and the peak quasi-static pressure loading on saturation duration and saturation deflection are discussed.It is found that there is a critical duration for the internal blast impulse to reach saturation,and beyond this duration,the deflection of plate will no longer increase as the loading increases further.The saturation deflection and saturation duration both exhibit regular variation patterns with the changes of the dimensionless peak shock wave,the duration of shock wave and the peak quasi-static pressure loading.展开更多
Impact and torsion pendulums are applied in impulse coupling experiments of high-energy laser irradiation of space debris. It is difficult to achieve a multi-pulse experiment and thus hard to analyze the multi-pulse i...Impact and torsion pendulums are applied in impulse coupling experiments of high-energy laser irradiation of space debris. It is difficult to achieve a multi-pulse experiment and thus hard to analyze the multi-pulse impulse coupling effect. Here, we designed a new recoil impulse experimental measurement system of non-contact, multidegrees of freedom, and multi-pulse irradiation. The system used a low-pressure and low-temperature vacuum chamber to simulate the space environment, the pinning effect of magnetic levitation to achieve aluminum target suspension, and high-speed cameras to record the displacement over time to calculate the impulse of the target.Then the impulse coupling experiment of multi-pulse laser irradiation on the aluminum target was performed.The result shows that the multi-pulse impulse coupling effect is not the linear accumulation of coupling results by every single-pulse and multi-pulse coefficient that decreases with the increase of the number of pulses, and eventually stabilizes as the decrease gets smaller.展开更多
In this paper,we investigate the dynamical behavior for a hybrid non-autonomous predator-prey system with Holling Type II functional response,impulsive effects and generalist predator on time scales,where our proposed...In this paper,we investigate the dynamical behavior for a hybrid non-autonomous predator-prey system with Holling Type II functional response,impulsive effects and generalist predator on time scales,where our proposed model commutes between a continuous-time dynamical system and discrete-time dynamical system.By using com--parison theorems,we first study the permanence results of the proposed model.Also,we established the uniformly asymptotic stability for the almost periodic solution of the proposed model.Finally,in the last section,we provide some examples with numerical simulation.展开更多
A mathematical model of a predator-prey model with Ivlev’s functional response concerning integrated pest management (IPM) is proposed and analyzed. We show that there exists a stable pest-eradication periodic soluti...A mathematical model of a predator-prey model with Ivlev’s functional response concerning integrated pest management (IPM) is proposed and analyzed. We show that there exists a stable pest-eradication periodic solution when the impulsive period is less than some critical values. Further more, the conditions for the permanence of the system are given. By using bifurcation theory, we show the existence and stability of a positive periodic solution. These results are quite different from those of the corresponding system without impulses. Numerical simulation shows that the system we consider has more complex dynamical behaviors. Finally, it is proved that IPM stragey is more effective than the classical one.展开更多
A stage-structured predator-prey system with impulsive effect and Holling type-II functional response is investigated. By the Floquet theory and small amplitude perturbation skills, it is proved that there exists a gl...A stage-structured predator-prey system with impulsive effect and Holling type-II functional response is investigated. By the Floquet theory and small amplitude perturbation skills, it is proved that there exists a global stable pest-eradication periodic solution when the impulsive period is less than some critical values. Farther, the conditions for the permanence of system are established. Numerical simulations are carried out to illustrate the impulsive effect on the dynamics of the system.展开更多
The general system of differential equations describing predator-prey dynamics with impulsive effects is modified by the assumption that the coefficients are periodic functions of time. By use of standard techniques o...The general system of differential equations describing predator-prey dynamics with impulsive effects is modified by the assumption that the coefficients are periodic functions of time. By use of standard techniques of bifurcation theory, it is known that this system has a positive periodic solution provided the time average of the predator’s net uninhibited death rate is in a suitable range. The bifurcation is from the periodic solution of the time-dependent logistic equation for the prey (which results in the absence of predator).展开更多
A mathematical model for the dynamics of a prey-dependent consumption model concerning integrated pest management is proposed and analyzed. We show that there exists a globally stable pesteradication periodic solution...A mathematical model for the dynamics of a prey-dependent consumption model concerning integrated pest management is proposed and analyzed. We show that there exists a globally stable pesteradication periodic solution when the impulsive period is less than some critical values. Furthermore, the conditions for the permanence of the system are given. By using bifurcation theory, we show the existence of a nontrival periodic solution if the pest-eradication periodic solution loses its stability. When the unique positive periodic solution loses its stability, numerical simulation shows there is a characteristic sequence of bifurcations, leading to a chaotic dynamics, which implies that dynamical behaviors of prey-dependent consumption concerning integrated pest management are very complex, including period-doubling cascades, chaotic bands with periodic windows, crises, symmetry-breaking bifurcations and supertransients.展开更多
This paper investigates the set stability of probabilistic time-delay Boolean networks(PTDBN)with impulsive effect.Firstly,using the algebraic state space representation,an equivalent stochastic system is established ...This paper investigates the set stability of probabilistic time-delay Boolean networks(PTDBN)with impulsive effect.Firstly,using the algebraic state space representation,an equivalent stochastic system is established for PTDBN with impulsive effect.Then,based on the probabilistic state transition matrix,a necessary and sufficient condition is presented for the set stability of PTDBN with impulsive effect.Finally,the obtained new result is applied to the networked evolutionary game with memories.展开更多
An Impulsive Multidirectional Associative Memory Neural Network(IMAMNN)with time-varying and leakage delays is proposed.Through the use of a continuation theorem of coincidence degree theory and differential inequalit...An Impulsive Multidirectional Associative Memory Neural Network(IMAMNN)with time-varying and leakage delays is proposed.Through the use of a continuation theorem of coincidence degree theory and differential inequality techniques we establish new conditions for the existence and exponential stability of anti-periodic solutions for the model considered in this work.Moreover,two examples and its numerical simulations are presented to show the validity and the effectiveness of the results.展开更多
基金Supported by the Natural Science Foundation of Guangdong Province (S2011010001900)the Guangdong Higher Education Foundation for High-Level Talents
文摘Results on the existence of piecewise continuous solutions for two classes of initial value problems of impulsive singular fractional differential equations are obtained.
基金Foundation item: Supported by the NNSF of China(11071254) Supported by the Science Foundation of Mechanical Engineering College(YJJXMll004)
文摘A delayed predator-prey model concerning impulsive spraying pesticides and releasing natural enemies is proposed and investigated,in which both the prey and the predator have a history that takes them through two stages:immature and mature.The global attractiveness of the pest-eradication periodic solution is discussed,and sufficient condition is obtained for the permanence of the system.Further,numerical simulations show that there is a characteristic sequence of bifurcations leading to a chaotic dynamics,which implies that the system with constant periodic impulsive perturbations admits rich and complex dynamics.
基金National Natural Science Foundations of China(No.11271371,No.10971229)
文摘The existence of homoclinic solutions for the second-order p-Laplacian differential system( ρ( t) Φp( u'( t))) '-s( t) Φp( u( t))+ λf( t,u( t)) = 0 with impulsive effects Δ( ρ( tj) Φp( u'( tj))) = Ij( u( tj)) is studied. By using three critical points theorem and variational methods, the sufficient condition is established to guarantee that this p-Laplacian differential system with impulsive effects has at least one nontrivial homoclinic solution. Besides,an example is presented to illustrate the main result in the end of this paper.
基金supported by the Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(Grant No.2013R1A1A2A10005201)the UAE University(Grant No.NRF Project UAEU-NRF-7-20886)
文摘We consider the impulsive effect on the exponential synchronization of neural networks with leakage delay under the sampled-data feedback control. We use an appropriate Lyapunov-Krasovskii functional combined with the input delay approach and some inequality techniques to derive sufficient conditions that ensure the exponential synchronization of the delayed neural network. The conditions are formulated in terms of the leakage delay, the sampling period, and the exponential convergence rate. Numerical examples are given to demonstrate the usefulness and the effectiveness of the results.
基金The authors would like to thank the support from the National Natural Science Foundation of China under Grant No.11802030.
文摘Under internal blast loading,the response of a beam or plate is highly correlated with the phenomenon of saturated impulse,which governs the deflection of the structure.This paper aims to investigate the phenomenon of saturated impulse for fully clamped rectangular plates subjected to internal blast loading.Based on the rigid,perfectly plastic assumption,the relationship between saturation duration and saturation deflection is derived.Influences of the peak shock wave,the duration of shock wave and the peak quasi-static pressure loading on saturation duration and saturation deflection are discussed.It is found that there is a critical duration for the internal blast impulse to reach saturation,and beyond this duration,the deflection of plate will no longer increase as the loading increases further.The saturation deflection and saturation duration both exhibit regular variation patterns with the changes of the dimensionless peak shock wave,the duration of shock wave and the peak quasi-static pressure loading.
文摘Impact and torsion pendulums are applied in impulse coupling experiments of high-energy laser irradiation of space debris. It is difficult to achieve a multi-pulse experiment and thus hard to analyze the multi-pulse impulse coupling effect. Here, we designed a new recoil impulse experimental measurement system of non-contact, multidegrees of freedom, and multi-pulse irradiation. The system used a low-pressure and low-temperature vacuum chamber to simulate the space environment, the pinning effect of magnetic levitation to achieve aluminum target suspension, and high-speed cameras to record the displacement over time to calculate the impulse of the target.Then the impulse coupling experiment of multi-pulse laser irradiation on the aluminum target was performed.The result shows that the multi-pulse impulse coupling effect is not the linear accumulation of coupling results by every single-pulse and multi-pulse coefficient that decreases with the increase of the number of pulses, and eventually stabilizes as the decrease gets smaller.
文摘In this paper,we investigate the dynamical behavior for a hybrid non-autonomous predator-prey system with Holling Type II functional response,impulsive effects and generalist predator on time scales,where our proposed model commutes between a continuous-time dynamical system and discrete-time dynamical system.By using com--parison theorems,we first study the permanence results of the proposed model.Also,we established the uniformly asymptotic stability for the almost periodic solution of the proposed model.Finally,in the last section,we provide some examples with numerical simulation.
基金Supported by National Natural Science Foundation of China (No.10171106)
文摘A mathematical model of a predator-prey model with Ivlev’s functional response concerning integrated pest management (IPM) is proposed and analyzed. We show that there exists a stable pest-eradication periodic solution when the impulsive period is less than some critical values. Further more, the conditions for the permanence of the system are given. By using bifurcation theory, we show the existence and stability of a positive periodic solution. These results are quite different from those of the corresponding system without impulses. Numerical simulation shows that the system we consider has more complex dynamical behaviors. Finally, it is proved that IPM stragey is more effective than the classical one.
基金Supported by the National Natural Science Foundation of China (Grant Nos.1067120910926064)
文摘A stage-structured predator-prey system with impulsive effect and Holling type-II functional response is investigated. By the Floquet theory and small amplitude perturbation skills, it is proved that there exists a global stable pest-eradication periodic solution when the impulsive period is less than some critical values. Farther, the conditions for the permanence of system are established. Numerical simulations are carried out to illustrate the impulsive effect on the dynamics of the system.
基金supported by National Natural Science Foundation of China 10171106
文摘The general system of differential equations describing predator-prey dynamics with impulsive effects is modified by the assumption that the coefficients are periodic functions of time. By use of standard techniques of bifurcation theory, it is known that this system has a positive periodic solution provided the time average of the predator’s net uninhibited death rate is in a suitable range. The bifurcation is from the periodic solution of the time-dependent logistic equation for the prey (which results in the absence of predator).
基金This work is supported by National Natural Science Foundation of China (10171106)supported by ScienceResearch Project Foundation of Liaoning Province Education Department
文摘A mathematical model for the dynamics of a prey-dependent consumption model concerning integrated pest management is proposed and analyzed. We show that there exists a globally stable pesteradication periodic solution when the impulsive period is less than some critical values. Furthermore, the conditions for the permanence of the system are given. By using bifurcation theory, we show the existence of a nontrival periodic solution if the pest-eradication periodic solution loses its stability. When the unique positive periodic solution loses its stability, numerical simulation shows there is a characteristic sequence of bifurcations, leading to a chaotic dynamics, which implies that dynamical behaviors of prey-dependent consumption concerning integrated pest management are very complex, including period-doubling cascades, chaotic bands with periodic windows, crises, symmetry-breaking bifurcations and supertransients.
基金supported by the National Natural Science Foundation of China under Grant No.71371186。
文摘This paper investigates the set stability of probabilistic time-delay Boolean networks(PTDBN)with impulsive effect.Firstly,using the algebraic state space representation,an equivalent stochastic system is established for PTDBN with impulsive effect.Then,based on the probabilistic state transition matrix,a necessary and sufficient condition is presented for the set stability of PTDBN with impulsive effect.Finally,the obtained new result is applied to the networked evolutionary game with memories.
文摘An Impulsive Multidirectional Associative Memory Neural Network(IMAMNN)with time-varying and leakage delays is proposed.Through the use of a continuation theorem of coincidence degree theory and differential inequality techniques we establish new conditions for the existence and exponential stability of anti-periodic solutions for the model considered in this work.Moreover,two examples and its numerical simulations are presented to show the validity and the effectiveness of the results.