共查询到20条相似文献，搜索用时 31 毫秒
1.
《Journal of The Franklin Institute》2022,359(18):10628-10652
Control of a water hyacinth-fish ecological system is required for a healthy and sustainable environment. This paper aims to investigate the global dynamics of a water hyacinth fish ecological system under ratio-dependent state impulsive control. First, we study the positivity and boundedness of the solution of the controlled system. By studying the local stability of the equilibrium, we find that the system has two situations. One is that there are two equilibria, namely a saddle point and a boundary equilibrium. In the second case, there are four equilibria, namely, two saddle points, a boundary equilibrium, and a focus point. For the first case, when we select an appropriate ratio-dependent control threshold, the trajectory will globally converge to the boundary equilibrium. For the second case, when the control line is located below the focus point, by using Poincare mapping method, flip bifurcation theory, and vector field analysis techniques, we find that the solution of the controlled system either globally converges to the boundary equilibrium, order-1 periodic solution, or order-2 periodic solution under certain conditions. When the control line is located above the focus point, the solution of the controlled system either globally converges to the focus point, order-1 or order-2 periodic solution. Finally, we use examples to verify the correctness and validity of the theoretical results. 相似文献
2.
《Journal of The Franklin Institute》2021,358(16):8656-8677
In this paper, a class of nonlocal Hopfield neural networks with random initial data is introduced, where the randomness may be of probability uncertainty. Sufficient conditions are derived to ensure the existence and globally exponential convergence of periodic solution for the addressed system in the frame of nonlinear expectation and linear expectation, respectively. Moreover, numerical examples are given to show the effectiveness of the obtained results. 相似文献
3.
Qun Liu Daqing Jiang Tasawar Hayat Ahmed Alsaedi 《Journal of The Franklin Institute》2018,355(13):5830-5865
In this paper, we study two stochastic multigroup S-DI-A epidemic models for the transmission of HIV. For the stochastic S-DI-A epidemic model with periodic coefficients, we first obtain sufficient conditions for persistence in the mean of the disease. Then in the case of persistence, we show that the model admits a positive T-periodic solution by using Khasminskii theory of periodic solution. Moreover, we establish sufficient conditions for exponential extinction of the infectious disease. For the stochastic S-DI-A epidemic model disturbed by both white and telegraph noises, we first establish sufficient conditions for persistence in the mean of the disease. Then in the case of persistence, we obtain sufficient conditions for the existence of a unique ergodic stationary distribution of the positive solutions by constructing a suitable stochastic Lyapunov function with regime switching and we also obtain sufficient conditions for exponential extinction of the system with regime switching. 相似文献
4.
A class of discrete-time cellular neural networks with complex deviating arguments and impulses are considered. Sufficient conditions for the existence of periodic solution are obtained by using contraction theorem and inequality techniques. The results of this paper are new. An example is employed to illustrate our results. 相似文献
5.
A solution of the periodic problem in a nonlinear system comprising a single-valued symmetric nonlinearity (Lure system) and linear dynamics is presented. The solution is designed as an iterative application of Periodic Signal Mapping to refine the approximate solution obtained through the describing function method. The algorithm is based upon the transformation of the original nonlinear system into an equivalent nonlinear system for which the filtering hypothesis is satisfied exactly, and for that reason the latter being suitable for application of the developed algorithm. The solution sought for is a fixed point of the periodic signal mapping. Conditions of asymptotic convergence of the proposed algorithm are given. The proposed approach is illustrated by two examples of analysis of periodic motions in a relay feedback system and chattering in a terminal sliding mode. 相似文献
6.
通过构造V函数法及细致的分析得到系统的一致持续性,在种群一致持续性前提下,利用Brouwer不动点定理证明系统至少存在一个正周期解,并通过构造Lyapunov泛函和运用微分不等式,稳定性理论及Barbalat’s引理得到了判定正周期解的全局渐近稳定性和全局吸引的充分条件。 相似文献
7.
The paper is indicated to constructing a modified conjugate gradient iterative (MCG) algorithm to solve the generalized periodic multiple coupled Sylvester matrix equations. It can be proved that the proposed approach can find the solution within finite iteration steps in the absence of round-off errors. Furthermore, we provide a method for choosing the initial matrices to obtain the least Frobenius norm solution of the system. Some numerical examples are illustrated to show the performance of the proposed approach and its superiority over the existing method CG. 相似文献
8.
Zhengqiu Zhang Guoqiang Peng Dongming Zhou 《Journal of The Franklin Institute》2011,348(10):2759-2781
In this paper, we investigate first the existence and uniqueness of periodic solution in a general Cohen–Grossberg BAM neural networks with delays on time scales by means of contraction mapping principle. Then by using the existence result of periodic solution and constructing a Lyapunov functional, we discuss the global exponential stability of periodic solution for above neural networks. In the last section, we also give examples to demonstrate the validity of our global exponential stability result of the periodic solution for above neural networks. 相似文献
9.
Bifurcation theory is commonly used to study the dynamical behavior of ecosystems. It involves the analysis of points in the parameter space where the stability of the system changes qualitatively. The type of bifurcation that associates equilibria with periodic solution is called Hopf bifurcation. In this paper, a life energy system dynamic model of two components with multiple delays is presented. It is shown that the interaction parameters of the delayed ecosystem play a fundamental role in classifying the rich dynamics and bifurcation phenomena. Regarding the combined interaction parameter as a bifurcation parameter, the bifurcation values in the parameter plane are displayed. The direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by applying the normal form theory and the center manifold theorem. Moreover, the amplitudes of oscillations always increase as the interaction parameters increase, while the robustness of periods occurs as the interaction parameters vary. From an ecological point of view, the existence of Hopf bifurcation expresses periodic oscillatory behavior of the life energy system. 相似文献
10.
恒化器是一个简单易于采用的用来培养微生物的实验装置。它被用做研究微生物的增长并有着对参数易于测量的优点。但是,关于恒化器模型的研究大都忽略了环境污染的情况。因此,本文考察在污染的环境中脉冲输入营养基Monod-Haldane恒化器模型．应用Floquet乘子理论和脉冲微分比较定理,得到微生物灭绝周期解是全局渐近稳定的充分条件,这意味着微生物培养失败。同时,得到在污染环境中微生物培养成功的条件,也就是系统持续生存的条件。最后讨论污染的环境对微生物培养的影响。 相似文献
11.
《Journal of The Franklin Institute》2022,359(9):4410-4432
The purpose of this paper is to present an iterative algorithm for solving the general discrete-time periodic Sylvester matrix equations. It is proved by theoretical analysis that this algorithm can get the exact solutions of the periodic Sylvester matrix equations in a finite number of steps in the absence of round-off errors. Furthermore, when the discrete-time periodic Sylvester matrix equations are consistent, we can obtain its unique minimal Frobenius norm solution by choosing appropriate initial periodic matrices. Finally, we use some numerical examples to illustrate the effectiveness of the proposed algorithm. 相似文献
12.
In this paper, we investigate an eco-epidemic model with distributed time delay and impulsive control strategy. Firstly, by using Floquet theory of impulsive differential equation, we get the condition for the local stability of the prey eradication periodic solutions. Secondly, by means of impulsive equation compare theory, we get the condition for the global asymptotical stability of the prey eradication periodic solutions. Finally we study the permanence of the system. Numerical simulations (bifurcation diagram, the largest Lyapunov exponents and power spectra) are carried out to illustrate the above theoretical analysis and the rich dynamics phenomenon, which are caused by impulsive effects and time delay, for example bifurcation, double period solution, etc. 相似文献
13.
This paper is concerned with the stability analysis of discrete-time linear systems with time-varying delays. The novelty of this paper lies in that a novel Lyapunov–Krasovskii functional that updates periodically along with the time is proposed to reduce the conservatism and eventually be able to achieve the non-conservativeness in stability analysis. It can be proved that the stability of a discrete-time linear delay system is equivalent to the existence of a periodic Lyapunov–Krasovskii functional. Two necessary and sufficient stability conditions in terms of linear matrix inequalities are proposed in this paper. Furthermore, the novel periodic Lyapunov–Krasovskii functional is employed to solve the ?2-gain performance analysis problem when exogenous disturbance is considered. The effectiveness of the proposed results is illustrated by several numerical examples. 相似文献
14.
Cooperative traffic systems renew much research interest with the rapid development of communication technologies. This paper considers a finite number of vehicles moving in a single lane from a mesoscale perspective and explores the spectral properties of such a cooperative system, in particular how the communication range and the coupling weights influence the eigenvalues of the global disturbance transition matrix (DTM), i.e., disturbance modes of the traffic system. Dynamics of these vehicles are described by a modified coupled-map car-following model under periodic boundaries with inter-vehicle communications. From a state-space approach, a system DTM is established from a global view and a closed-form solution of its eigenvalues is derived. Linear stability conditions are subsequently obtained. It is found that the eigenvalue distribution of system DTM is essentially dominated by the communication range and the coupling weights, but nearly independent of the system size. By analyzing the magnitudes of the dominant poles, the synchronization of the traffic system is enhanced if the weights of the vehicles within the communication range are more evenly distributed or the communication range is increased. Particularly, it is shown that the optimal communication network tends to be a mean-field network w.r.t. global synchronization, indicating that a communication network emphasizing uniform importance among vehicles within each vehicle’s communication range is helpful for improving the synchronizability. Finally, numerical simulations verify the results. 相似文献
15.
Lingling Lv Jinbo Chen Zhe Zhang Baowen Wang Lei Zhang 《Journal of The Franklin Institute》2021,358(3):2039-2059
This paper studies the numerical solutions of a class of periodic coupled matrix equations. Based on the least square method, a finite iterative algorithm for a class of periodic coupled matrix equations is proposed, and the convergence of the algorithm is proved by theoretical derivation. For any initial value, the algorithm can converge to the solution in finite iterations. Since the equations considered in paper contain many variants, the proposed algorithm has a wide range of applications. Finally some numerical examples in practical systems are given to prove the effectiveness and efficiency of the algorithm. 相似文献
16.
史远军 《中国科学院研究生院学报》1997,(1)
在二阶系统一系列定理基础上,建立一个直接根据系统Lyapunov函数性质判定系统周期解存在性的定理,针对一类二阶非自治非线性系统构造了适当的Lyapunov函数,并研究了这类系统周期解的存在性。 相似文献
17.
Qiankun Song 《Journal of The Franklin Institute》2008,345(1):39-59
In this paper, the discrete-time fuzzy cellular neural network with variable delays and impulses is considered. Based on M-matrix theory and analytic methods, several simple sufficient conditions checking the global exponential stability and the existence of periodic solutions are obtained for the neural networks. Moreover, the estimation for exponential convergence rate index is proposed. The obtained results show that the stability and periodic solutions still remain under certain impulsive perturbations for the neural network with stable equilibrium point and periodic solutions. Some examples with simulations are given to show the effectiveness of the obtained results. 相似文献
18.
19.
《Journal of The Franklin Institute》2022,359(14):7733-7752
In this paper, the networked stabilization of discrete-time periodic piecewise linear systems under transmission package dropouts is investigated. The transmission package dropouts result in the loss of control input and the asynchronous switching between the subsystems and the associated controllers. Before studying the networked control, the sufficient conditions of exponential stability and stabilization of discrete-time periodic piecewise linear systems are proposed via the constructed dwell-time dependent Lyapunov function with time-varying Lyapunov matrix at first. Then to tackle the bounded time-varying packet dropouts issue of switching signal in the networked control, a continuous unified time-varying Lyapunov function is employed for both the synchronous and asynchronous subintervals of subsystems, the corresponding stabilization conditions are developed. The state-feedback stabilizing controller can be directly designed by solving linear matrix inequalities (LMIs) instead of iterative optimization used in continuous-time periodic piecewise linear systems. The effectiveness of the obtained theoretical results is illustrated by numerical examples. 相似文献
20.
Chang Liu Yuru Guo Hongxia Rao Ming Lin Yong Xu 《Journal of The Franklin Institute》2021,358(4):2367-2381
Finite-time (FT) synchronization for periodic T–S fuzzy master-slave neural networks (NNs) with distributed delays is addressed in this work. A fuzzy controller is designed for the salve NNs to synchronize the master NNs in FT and a synchronization error system (SES) is derived. Sufficient conditions are established to guarantee that the SES is FT bounded by using the mode and fuzzy basis dependent Lyapunov function. A new algorithm is proposed to obtain the suboptimal boundary of the SES to analyze how the periodic characteristics affect the system boundary. Finally, a numerical example is provided to demonstrate the validity of the fuzzy controller and the iterative algorithm for the boundary. 相似文献