Globally exponentially stable periodic solution in a general delayed predator-prey model under discontinuous prey control strategy

Abstract

This paper studies the solution behaviour of a general delayed predator-prey model with discontinuous prey control strategy. The positiveness and boundeness of the solution of the system is firstly investigated using the comparison theorem. Then the sufficient conditions are derived for the existence of positive periodic solutions using the differential inclusion theory and the topological degree theory. Furthermore, the positive periodic solution is proved to be globally exponentially stable by employing the generalized Lyapunov approach. The global finite-time convergence is also discussed for the system state. Finally, the numerical simulations of four examples are given to validate the correctness of the theoretical results.

Global dynamics and bifurcations of Filippov SIR epidemic model with general nonlinear transmission and discontinuous control

“…Currently, many control management have been developed, including T.C. [9,12,21,25,28,34,41,45,46], H.C. [14,23,24] and I.C. [22,25,26,44] and the other control [1,3,10,18,40,42].…”

Periodicity on Neutral-Type Inertial Neural Networks Incorporating Multiple Delays

“…It is well known that the classical Hopefield neural networks have obvious symmetry, numerous researchers have carried out extensive research on its related dynamic behaviors [16,[22][23][24]. In particular, the authors in [25] investigate the exponential stability and the almost sure exponential stability for a class of stochastic fuzzy Cohen-Grossberg neural networks by fabricating an appropriate Lyapunov functional.…”

“…It should be pointed out that in addition to the state itself, there are also time delays in the derivatives of the state related to the networks. This kind of delay is deemed as neutral delay, which not only appears in the field of automatic control and population ecology [26,27], but also occurs in many physical systems, including transmission lines, Lotka-Volterra systems, chemical reactors, and others [23,24,28,29]. Particularly, if we use differential equations to model neural networks (NNs) for the realization of electronic circuits, the influence of neutral delay often exists.…”

“…Particularly, if we use differential equations to model neural networks (NNs) for the realization of electronic circuits, the influence of neutral delay often exists. The authors in [24,29] investigated the effect of neutral delays on the partial element equivalent circuit. The circuit was represented to a neutral-type functional differential equation, and some new sufficient stability assertions were given by Lyapunov theory.…”

“…Especially in the application of NNs, periodic phenomenon is one of the most important dynamic behaviors to describe the symmetry of the Hopefield neural networks model, and the existence and stability of periodic solutions will help us to understand the asymptotic behavior of mathematical biological systems. Therefore, it is a very meaningful thing to research the existence and stability of periodic solutions [24,32]. However, few researches have discussed the periodic problem of the following NTINNs involving multiple delays:…”