Dynamic analysis on an almost periodic predator-prey system with impulsive effects and time delays

Abstract

This article is concerned with a generalized almost periodic predatorprey model with impulsive effects and time delays. By utilizing comparison theorem and constructing a feasible Lyapunov functional, we obtain sufficient conditions to guarantee the permanence and global asymptotic stability of the system. By applying Arzelà-Ascoli theorem, we establish the existence and uniqueness of almost-periodic positive solutions. A feasible numerical simulation is provided to explain the suitability of our main criteria.

Lyapunov Approach for Almost Periodicity in Impulsive Gene Regulatory Networks of Fractional Order with Time-Varying Delays

“…The almost periodicity concepts defined in Definitions 5-7 are adopted from [38,39]. Similar notions are applied in [35,[40][41][42][43][44][45]. We will refer the reader to [49,50] for more details and definitions of almost periodic sequences and functions.…”

“…The practical meaning of our conclusions is that when the translation rates, basal rates, and the connecting parameters in the considered fractional impulsive GRN are variable (not constants) but bounded, and the magnitudes of the impulsive perturbations satisfy conditions of Theorem 2, then the model is capable to generate a unique globally Mittag-Leffler stable almost periodic process. Indeed, the concept of almost periodicity has deep historical roots [36] and has important applications in applied mathematical models [35,[39][40][41][42]47,48]. Indeed, it is an unrealistic assumption that the behavior of the states in the GRNs are not affected by periodical environmental factors.…”

“…On the importance of studying of almost periodic properties and processes we will direct readers to [35][36][37][38][39]. This is the main reason of the existing of numerous results on almost periodicity of different classes of applied problems [40][41][42], including fractional neural networks [43][44][45]. In fact, the non-existence of pure periodic solutions for systems of fractional order has been proved in [46].…”

Dynamic analysis of a Leslie–Gower-type predator–prey system with the fear effect and ratio-dependent Holling III functional response

“…As one of the most common mutual relationships between two populations in nature, predator-prey relationship plays a significant role in ecology and mathematical biology [2]. Since the dynamic behaviours of predator-prey models were formulated by Lotka and Volterra, many experts and scholars have studied various types of predator-prey models over the past decades, thus establishing the theoretical basis for interspecific interactions [1,4,12,14]. In 1948, Leslie and Gower introduced a functional response called Leslie-Gower, which was based on the Logistic model proposed by Verhulst.…”

Impulsive Fractional Differential Inclusions and Almost Periodic Waves

“…The almost periodic properties also have an important value in impulsive differential systems, and the analysis of the impulsive effects on the almost periodic behavior of solutions to such integer [38][39][40][41][42] and fractional-order [43][44][45][46][47] systems has received significant attention. Therefore, their effects on the almost periodic behavior of fractional-order inclusions should be further investigated.…”