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Lansun Chen - One of the best experts on this subject based on the ideXlab platform.
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a novel method for analyzing the stability of Periodic Solution of impulsive state feedback model
Applied Mathematics and Computation, 2016Co-Authors: Mingjing Sun, Yinli Liu, Sujuan Liu, Lansun ChenAbstract:The complex dynamics on the single population model with impulsively unilateral diffusion between two patches was studied in a theoretical way. The existence, uniqueness and stability of an order-1 Periodic Solution was investigated for state-dependent impulsively differential equations. The sufficient conditions for the existence and stability of positive Periodic Solution were obtained using the Poincare map by comparison with the analysis for limit cycles of continuous systems, which was different from the analogue of Poincare criterion. Meanwhile, the uniqueness of Periodic Solution was proofed by the monotone of successor function.
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Periodic Solution of the system with impulsive state feedback control
Nonlinear Dynamics, 2014Co-Authors: Guoping Pang, Lansun ChenAbstract:The order-1 Periodic Solution of the system with impulsive state feedback control is investigated. We get the sufficient condition for the existence of the order-1 Periodic Solution by differential equation geometry theory and successor function. Further, we obtain a new judgement method for the stability of the order-1 Periodic Solution of the semi-continuous systems by referencing the stability analysis for limit cycles of continuous systems, which is different from the previous method of analog of Poincare criterion. Finally, we analyze numerically the theoretical results obtained.
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Periodic Solution and heteroclinic bifurcation in a predator prey system with allee effect and impulsive harvesting
Nonlinear Dynamics, 2014Co-Authors: Chunjin Wei, Lansun ChenAbstract:In this article, we investigate a prey– predator model with Allee effect and state-dependent impulsive harvesting. We obtain the sufficient conditions for the existence and uniqueness of order-1 Periodic Solution of system (1.2) by means of the geometry theory of semicontinuous dynamic system and the method of successor function. We also obtain that system (1.2) exhibits the phenomenon of heteroclinic bifurcation about parameter \(\alpha \). The methods used in this article are novel and prove the existence of order-1 Periodic Solution and heteroclinic bifurcation.
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geometric approach to the stability analysis of the Periodic Solution in a semi continuous dynamic system
International Journal of Biomathematics, 2014Co-Authors: Yuan Tian, Kaibiao Sun, Lansun ChenAbstract:Integrated pest management (IPM) is a long-term management strategy and has been proved to be more effective in pest control. To well-understand the mechanism and effect of the action of IPM, the geometric theory of the involved semi-continuous dynamic systems is becoming more and more important. In this work, a geometric approach is applied to analyze the stability of the positive order-one Periodic Solution in semi-continuous dynamic systems. A stability criterion to test the stability of the order-one Periodic Solution is established. As an application, a stage-structure model involved chemical control is presented to show the efficiency of the proposed method. The sufficient conditions to insure the existence of the Periodic Solution are provided. In addition, the number and the stability of the Periodic Solutions are discussed accordingly. The simulations are carried out to verify the results.
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Periodic Solution of prey predator model with beddington deangelis functional response and impulsive state feedback control
Journal of Applied Mathematics, 2012Co-Authors: Lansun ChenAbstract:A prey-predator model with Beddington-DeAngelis functional response and impulsive state feedback control is investigated. We obtain the sufficient conditions of the global asymptotical stability of the system without impulsive effects. By using the geometry theory of semicontinuous dynamic system and the method of successor function, we obtain the system with impulsive effects that has an order one Periodic Solution, and sufficient conditions for existence and stability of order one Periodic Solution are also obtained. Finally, numerical simulations are performed to illustrate our main results.
Jinde Cao - One of the best experts on this subject based on the ideXlab platform.
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anti Periodic Solution for delayed cellular neural networks with impulsive effects
Nonlinear Analysis-real World Applications, 2011Co-Authors: Lijun Pan, Jinde CaoAbstract:Abstract In this paper, we discuss anti-Periodic Solution for delayed cellular neural networks with impulsive effects. By means of contraction mapping principle and Krasnoselski’s fixed point theorem, we obtain the existence of anti-Periodic Solution for neural networks. By establishing a new impulsive differential inequality, using Lyapunov functions and inequality techniques, some new results for exponential stability of anti-Periodic Solution are obtained. Meanwhile, an example and numerical simulations are given to show that impulses may change the exponentially stable behavior of anti-Periodic Solution.
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existence and attractivity of almost Periodic Solution for recurrent neural networks with unbounded delays and variable coefficients
Nonlinear Dynamics, 2006Co-Authors: Xia Huang, Jinde CaoAbstract:This paper presents several sufficient conditions for the existence and attractivity of almost Periodic Solution for a new class of recurrent neural networks with unbounded delays and variable coefficients. Different from the normal approach, that's to say, without resorting to any Lyapunov function, these results are obtained by utilizing generalized Halanay inequality technique and combining the theory of exponential dichotomy with fixed point method. Some existing results are found to be special case of this paper. In addition, the exponential stability of the almost Periodic Solution, which is not studied in the earlier references, is also considered for the system. An example is given to illustrate the feasibility of our results.
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almost Periodic Solution of shunting inhibitory cellular neural networks with time varying delay
Physics Letters A, 2003Co-Authors: Xia Huang, Jinde CaoAbstract:Several sufficient conditions are obtained for the existence of almost Periodic Solution and its attractivity of shunting inhibitory cellular neural networks with time-varying delay based on the fixed point method and Halanay inequality technique. Some previous results are improved and extended in this Letter and two examples are given to illustrate the effectiveness of the new results.
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existence and stability of almost Periodic Solution for bam neural networks with delays
Applied Mathematics and Computation, 2003Co-Authors: Anping Chen, Lihong Huang, Jinde CaoAbstract:By using the Banach fixed point theorem and constructing suitable Lyapunov function, some sufficient conditions are obtained ensuring existence, uniqueness and global stability of almost Periodic Solution of the BAM neural networks with variable coefficients and delays. These results are helpful to design global exponential stable BAM networks and almost Periodic oscillatory BAM networks.
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almost Periodic Solution of shunting inhibitory cnns with delays
Physics Letters A, 2002Co-Authors: Anping Chen, Jinde CaoAbstract:Abstract Using the Banach fixed point theorem, we obtain a sufficient condition for the existence of almost Periodic Solution of shunting inhibitory cellular neural networks dx ij dt =−a ij x ij − ∑ C kl ∈N r (i,j) C ij kl f x kl (t−τ) x ij +L ij (t), the global attractivity of SICNNs is also obtained. An example is given to illustrate that the condition of our results are feasible.
Hongjun Xiang - One of the best experts on this subject based on the ideXlab platform.
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almost Periodic Solution of cohen grossberg neural networks with bounded and unbounded delays
Nonlinear Analysis-real World Applications, 2009Co-Authors: Hongjun XiangAbstract:Abstract In this paper, a class of Cohen–Grossberg neural networks with bounded and unbounded delays is discussed. Several new sufficient conditions are obtained ensuring the existence and exponential stability of the almost Periodic Solution for this model based on inequality analysis technique and combing the exponential dichotomy with fixed point theorem. The obtained results are helpful to design globally exponentially stable almost Periodic oscillatory neural networks. Two numerical examples and simulations are also given to show the feasibility of our results.
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exponential stability of Periodic Solution to cohen grossberg type bam networks with time varying delays
Neurocomputing, 2009Co-Authors: Hongjun XiangAbstract:Periodic Solutions can represent various storage patterns or memory patterns in some applications. In this paper, the existence and global exponential stability of Periodic Solution are discussed for the Cohen-Grossberg-type bidirectional associative memory (BAM) neural networks with time-varying delays. By applying the analysis method and inequality technique, some novel sufficient conditions are obtained to ensure the existence, uniqueness, global attractivity and exponential stability of the Periodic Solution to the considered system. Moreover, two examples are also given to demonstrate the feasibility of the obtained results.
Zhijun Liu - One of the best experts on this subject based on the ideXlab platform.
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Periodic Solution of a chemostat model with variable yield and impulsive state feedback control
Applied Mathematical Modelling, 2012Co-Authors: Lansun Chen, Zhijun LiuAbstract:Abstract In this paper, a chemostat model with variable yield and impulsive state feedback control is considered. We obtain sufficient conditions of the globally asymptotical stability of the system without impulsive state feedback control. We also obtain that the system with impulsive state feedback control has Periodic Solution of order one. Sufficient conditions for existence and stability of Periodic Solution of order one are given. In some cases, it is possible that the system exists Periodic Solution of order two. Our results show that the control measure is effective and reliable.
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Periodic Solution of a two species competitive system with toxicant and birth pulse
Chaos Solitons & Fractals, 2007Co-Authors: Zhijun Liu, Lansun ChenAbstract:In this paper, we study the existence of positive Periodic Solution of two-species competitive system with toxicant and birth pulse. A set of easily verifiable sufficient conditions are derived for the existence of at least one positive Periodic Solution of the above system by using the method of coincidence degree. Numerical simulations are also presented to illustrate the feasibility of our main results.
Daqing Jiang - One of the best experts on this subject based on the ideXlab platform.
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nontrivial Periodic Solution for a stochastic brucellosis model with application to xinjiang china
Physica A-statistical Mechanics and Its Applications, 2018Co-Authors: Lei Wang, Daqing Jiang, Tasawar Hayat, Kai WangAbstract:Abstract Brucellosis is a kind of zoonotic disease caused by Gram-negative bacteria of the genus Brucella. In this paper, we propose a stochastic Periodic brucellosis model by introducing the effect of environmental white noise on transmission dynamics of brucellosis. By Has’minskii theory of Periodic Solution and constructing a novel combination of Lyapunov functions, we establish the existence of nontrivial positive Periodic Solution if the condition R 0 S > 1 holds. Based on the reported data of newly acute human brucellosis cases for each season from 2010 to 2014 in Xinjiang, numerical simulations have been performed to support our result and indicate that brucellosis in Xinjiang takes on the feature of long-term prevalence and cyclical fluctuation.
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Periodic Solution and stationary distribution of stochastic s di a epidemic models
Applicable Analysis, 2018Co-Authors: Xinhong Zhang, Daqing Jiang, Tasawar Hayat, Ahmed AlsaediAbstract:AbstractThis paper considers two S-DI-A models in random environments. Firstly, using Has’minskii theory of Periodic Solution, we show that stochastic Periodic S-DI-A model has a nontrivial positive Periodic Solution if . Then, we construct stochastic Lyapunov functions with regime switching to obtain the existence of ergodic stationary distribution of the Solution to S-DI-A model perturbed by white and telephone noises. Finally, examples are introduced to illustrate the results developed.
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Periodic Solution and stationary distribution of stochastic sir epidemic models with higher order perturbation
Physica A-statistical Mechanics and Its Applications, 2017Co-Authors: Daqing Jiang, Tasawar Hayat, Qun Liu, Bashir AhmadAbstract:In this paper, we investigate two stochastic SIR epidemic models with higher order perturbation. For the nonautonomous Periodic case of the model, by using Has’minskii’s theory of Periodic Solution, we show that the system has at least one nontrivial positive T-Periodic Solution. For the system disturbed by both the white noise and telephone noise, we establish sufficient conditions for positive recurrence and the existence of ergodic stationary distribution of the positive Solution.
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Periodic Solution for a stochastic non autonomous competitive lotka volterra model in a polluted environment
Physica A-statistical Mechanics and Its Applications, 2017Co-Authors: Daqing Jiang, Tasawar Hayat, Qiumei Zhang, Ahmed AlsaediAbstract:In this paper, we consider a stochastic non-autonomous competitive Lotka–Volterra model in a polluted environment. We derive sufficient criteria for the existence and global attractivity of the boundary Periodic Solutions. Furthermore, we obtain conditions for the existence and global attractivity of a nontrivial positive Periodic Solution. Finally we make simulations to illustrate our analytical results.
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Periodic Solution for a stochastic nonautonomous SIR epidemic model with logistic growth
Physica A: Statistical Mechanics and its Applications, 2016Co-Authors: Qun Liu, Ningzhong Shi, Daqing Jiang, Tasawar Hayat, Ahmed AlsaediAbstract:In this paper, we analyze the dynamics of a stochastic nonautonomous SIR epidemic model, in which population growth is subject to logistic growth in absence of disease. For the Periodic system, we present sufficient conditions for persistence of the epidemic and in the case of persistence, by constructing some suitable Lyapunov functions, we show that there is at least one nontrivial positive Periodic Solution. One of the most important findings is that random perturbations may be beneficial to formate the Periodic Solution to the stochastic nonautonomous SIR epidemic model.
