Narrow Results

Sufficient conditions are obtained for the existence and global exponential stability of a unique periodic solution of a class of impulsive tow-neuron networks with variable and unbounded delays. The approaches are based on Mawhin's continuation theorem of coincidence degree theory and Lyapunov functions.

In this paper, the impulsive Cohen-Grossberg neural network with unbounded discrete time-varying delays is considered. By using the analysis method and inequality technique, several sufficient conditions are obtained to ensure the global exponential stability of the addressed neural network. These results generalize the existing relevant stability results. Two examples with simulations are given to show the effectiveness of the obtained results.

This research is aimed at investigating the leader–follower problem of third-order multi-agent with noise perturbation over fixed network under impulsive and switching control. Based on stochastic differential equation theory and hybrid control theory, effective impulsive and switching controllers are proposed, and the sufficient conditions for reaching multi-agent leader-following consensus are acquired. Numerical simulations verify the validity of the theoretical research results.

The convergent dynamical behaviors of a class of impulsive integro-differential equation are discussed. By establishing an integro-differential inequality with impulsive initial conditions and using the properties of M-cone and eigenspace of the spectral radius of non-negative matrices, some new sufficient conditions to guarantee the global exponential stability are obtained. The results extend and improve the earlier publications. An example is given to illustrate the theoretical results.

In this work, we consider a logistic fishery model and discuss the selective impulsive harvesting of fish above a certain age or size by incorporating a time delay in the impulsive harvesting term. It is proved that there exists an asymptotically stable positive periodic solution when the catchability coefficient h is less than some critical value . It is concluded that and are increasing with respect to l. Simulations shows that the delayed harvesting is advantageous to the sustainability of the population.

This paper is concerned with the asymptotic behaviors of the solutions of an impulsive stochastic neural field lattice model driven by nonlinear noise. We first show the existence and uniqueness of weak pullback mean random attractors for the impulsive stochastic systems. Then by the properties of Markov processes, the existence of evolution system of measures for the impulsive stochastic systems is established. To this end, we employ the idea of uniform estimates on the tails of the solutions to show the tightness of a family of distributions of the solutions of the lattice systems.

This paper is devoted to the investigation of the oscillation of a class of second-order nonlinear impulsive delay difference equations. Some interesting results are obtained, and some examples which illustrate that impulsive perturbations play a very important role in giving rise to oscillations of equations are also included.

In this work, we consider a stage-structured pest management SI model with time delay and diseased pests impulsive transmission. Sufficient conditions which guarantee the global attractivity of pest-extinction periodic solution and permanence of the system are obtained. We also prove that all solutions of the system are uniformly ultimately bounded. Our results provide reliable tactic basis for the practical pest management.

In this work, we consider a delayed stage-structured variable coefficients predator-prey system with impulsive perturbations on predators. By using the discrete dynamical system determined by stroboscopic map and the standard comparison theorem, we obtain the sufficient conditions which guarantee the global attractivity of prey-extinction periodic solution of the investigated system. We also prove that all solutions of the system are uniformly ultimately bounded. Our results provide reliable tactic basis for the practical pest management.

In this paper, an impulsive exploitation of single species modelled by a general nonautonomous equation is considered. The persistence of the population can be obtained under sufficiently weak conditions and also be distinguished from conditions that cause extinction. These attributes resemble corresponding features of the related autonomous population growth model and improve the results of [6–8].

In the paper, according to biological and chemical control strategy for pest control, our main purpose is to construct a three trophic level food chain system with Holling IV functional responses and periodic constant impulsive effect concerning integrated pest management (IPM), and investigate the dynamic behaviors of this system. By using the Floquet theory and comparison theorem of impulsive differential equation and analytic method, we prove that there exists a globally asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical value. Further, condition for permanence of the system is established. Finally, numerical simulation shows that there exists a stable positive periodic solution with a maximum value no larger than a given level.

In this paper, we introduce and study an impulsive mutualistic model with variable coefficients. By using Floquent theorem, the invasion threshold and the stability of the boundary periodic solution are obtained. Furthermore, by using standard techniques of bifurcation theory, the existent condition of the positive periodic solution is obtained. Finally, numerical simulations are carried out to confirm the main theorems.

This paper deals with the problem of asymptotical stability in mean square for a class of impulsive stochastic high-order bi-directional associative memory (BAM) neural networks with mixed delays and Markovian jumping parameters. Based on Lyapunov stability theory, linear matrix inequality and mathematical induction, some sufficient conditions are derived for the asymptotical stability in mean square of the equilibrium point of the neural networks. The results obtained in this paper are new and complement previously known results.

In this paper, a model of Beddington–DeAngelies chemostat involving two species of micro-organism competing for two perfectly complementary growth-limiting nutrients and pulsed input of toxicant in the polluted environment was studied. Using Floquet theory and small amplitude perturbation method, a conclusion was that there exists two-micro-organism eradication periodic solution and which is global asymptotical stability. At the same time, the condition of the permanence for system was obtained. From the biological point of view, the method for protecting species is to improve the amount of impulsive period, and control the amount of toxicant input to the chemostat. Finally, our results are illustrated by numerical simulations.

A class of time-varying delay impulsive reaction–diffusion tree–grass–water–nitrogen system driven by Lévy jump process is considered. First, we prove the existence and uniqueness of the global positive solution of the model by constructing the Lyapunov function. Secondly, several sufficient conditions for finite-time stability are given by using comparison theorem and mean impulse interval method. Finally, numerical simulations are carried out to verify the effectiveness of the theoretical analysis.

In this paper, we study the existence of mild solutions of impulsive evolution fractional functional differential equation of order $0<\alpha <1$ involving a Lipschitz condition on term $I_k$. We shall rely on a fixed point theorem for the sum of completely continuous and contraction operators due to Burton and Kirk.

In this paper, we investigate the existence of periodic solution of impulsive bidirectional associative memory (BAM) networks on time scales. By using the nonlinear alternative of Leray-Schauder fixed point theorem, we show that there exists a periodic solution of BAM networks under bounded impulsive perturbation. The results are new and never reported in the literature.