Exponential ultimate boundedness of non-autonomous fractional differential systems with time delay and impulses

Xu, Liguang; Chu, Xiaoyan; Hu, Hongxiao

doi:10.1016/j.aml.2019.106000

Cited by 34 publications

(7 citation statements)

References 11 publications

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“…This paper only focuses on the coupled space fractional Ginzburg-Landau equations, where time delay is ignored. As is well known, time delay has been receiving considerable attention and eliciting widespread interest [33][34][35][36][37]. However, the coupled space fractional Ginzburg-Landau equations is a nonlinear system, the convergence analysis for the timedelay case is not a matter of standard error analysis.…”

Section: Resultsmentioning

confidence: 99%

A fourth-order linearized difference scheme for the coupled space fractional Ginzburg–Landau equation

Yuan

Zeng

2019

Adv Differ Equ

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In this paper, the coupled space fractional Ginzburg-Landau equations are investigated numerically. A linearized semi-implicit difference scheme is proposed. The scheme is unconditionally stable, fourth-order accurate in space, and second-order accurate in time. The optimal pointwise error estimates, unique solvability, and unconditional stability are obtained. Moreover, Richardson extrapolation is exploited to improve the temporal accuracy to fourth order. Finally, numerical results are presented to confirm the theoretical results.

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Section: Resultsmentioning

confidence: 99%

A fourth-order linearized difference scheme for the coupled space fractional Ginzburg–Landau equation

Yuan

Zeng

2019

Adv Differ Equ

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“…), and x(t + ) = lim t→t + x(t) exists, where t = (2k + 1)ω (or (2k + 2)ω). Clearly, the existence and uniqueness of solution of model ( 4) can be guaranteed by the smoothness properties of the right-hand side of model ( 4) ( [19][20][21][22]). The proof of the positivity of any solution (x(t), y(t)) of model ( 4) with any initial value (x(0), y(0)) ∈ R 2 + = {(x, y) | x > 0, y > 0} is so easy that we omit it.…”

Section: Preliminariesmentioning

confidence: 99%

“…Here ξ = max 0<x≤M { Φ1 (x)M, Φ2 (x)M}. From Lemma 2.2, we have x(t) ≥ u(t), where u(t) is the solution of the following system (22)…”

Section: Theorem 33 If (H 1 )-(H 3 ) Hold Andmentioning

confidence: 99%

A hybrid predator–prey model with general functional responses under seasonal succession alternating between Gompertz and logistic growth

et al. 2020

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In this paper, a hybrid predator–prey model with two general functional responses under seasonal succession is proposed. The model is composed of two subsystems: in the first one, the prey follows the Gompertz growth, and it turns to the logistic growth in the second subsystem since seasonal succession. The two processes are connected by impulsive perturbations. Some very general, weak criteria on the ultimate boundedness, permanence, existence, uniqueness and global attractivity of predator-free periodic solution are established. We find that the hybrid population model with seasonal succession has more survival possibilities of natural species than the usual population models. The theoretical results are illustrated by special examples and numerical simulations.

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“…[27], [28]). Noting that impulsive phenomena exist widespread in reality, impulsive differential systems are introduced to describe real systems with impulsive phenomena, and have wide applications in the fields of control, economics and biology [29]- [31], [33], [36]. There are many works on impulsive systems with stochastic factors (e.g.…”

Section: Introductionmentioning

confidence: 99%

Noises for Impulsive Differential Systems

Hao

Feng

2019

IEEE Access

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Stochastic feedback control has aroused folks' notice, but little is known on the roles of stochastic noises for the dynamic behavior of impulsive differential systems. In this paper, we mainly study the problem of stochastic stabilization on explosive solutions of nonlinear impulsive differential systems by noises. Under the one-sided polynomial growth condition, a nonlinear impulsive differential system may explode at a finite time. To suppress the explosive solution, we introduce two independent stochastic noises (polynomial and linear) such that there exists a unique global solution for the corresponding stochastically perturbed impulsive differential system, and the global solution is bounded and almost surely exponentially stable.

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Exponential ultimate boundedness of non-autonomous fractional differential systems with time delay and impulses

Cited by 34 publications

References 11 publications

A fourth-order linearized difference scheme for the coupled space fractional Ginzburg–Landau equation

A fourth-order linearized difference scheme for the coupled space fractional Ginzburg–Landau equation

A hybrid predator–prey model with general functional responses under seasonal succession alternating between Gompertz and logistic growth

Noises for Impulsive Differential Systems

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