scholarly journals Almost periodic solutions of a discrete Lotka-Volterra model via exponential dichotomy theory

2021 ◽  
Vol 7 (3) ◽  
pp. 3788-3801
Author(s):  
Lini Fang ◽  
◽  
N'gbo N'gbo ◽  
Yonghui Xia
Keyword(s):  
Fixed Point ◽  
Periodic Solutions ◽  
Exponential Dichotomy ◽  
Exponential Convergence ◽  
Volterra Model ◽  
Banach Fixed Point Theorem ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
The Difference ◽  
Positive Almost Periodic Solutions

<abstract><p>In this paper, we consider a discrete non-autonomous Lotka-Volterra model. Under some assumptions, we prove the existence of positive almost periodic solutions. Our analysis relies on the exponential dichotomy for the difference equations and the Banach fixed point theorem. Furthermore, by constructing a Lyapunov function, the exponential convergence is proved. Finally, a numerical example illustrates the effectiveness of the results.</p></abstract>

scholarly journals Mean-Square Almost Periodic Solutions for Impulsive Stochastic Host-Macroparasite Equation on Time Scales

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Pan Wang ◽  
Qingmei Lin ◽  
Yongkun Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Time Scales ◽  
Banach Fixed Point Theorem ◽  
Mean Square ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Inequality Technique ◽  
Bellman’S Inequality

We consider an impulsive stochastic host-macroparasite equation on time scales. By use of the Banach fixed point theorem and Gronwall-Bellman’s inequality technique on time scales, we obtain the existence and exponential stability of mean-square almost periodic solutions for the host-macroparasite equation on time scales. Finally, we give an example to illustrate the feasibility of our results.

scholarly journals On the Positive Almost Periodic Solutions of a Class of Nonlinear Lotka-Volterra Type System with Feedback Control

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Ni Hua ◽  
Tian Li-Xin ◽  
Yao Hong-Xing
Keyword(s):  
Fixed Point ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Type System ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Volterra Type ◽  
Variable Substitution ◽  
The Fixed Point Theorem ◽  
Positive Almost Periodic Solutions

With the help of the variable substitution and applying the fixed point theorem, we derive the sufficient conditions which guarantee the existence of the positive almost periodic solutions for a class of Lotka-Volterra type system. The main results improve and generalize the former corresponding results.

scholarly journals Asymptotically almost periodic solutions of fractional relaxation inclusions with Caputo derivatives

2018 ◽  
Vol 104 (118) ◽  
pp. 23-41 ◽  
Author(s):  
Marko Kostic
Keyword(s):  
Fixed Point ◽  
Periodic Solutions ◽  
Fixed Point Theorems ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Periodic Coefficients ◽  
Sectorial Operators ◽  
Almost Sectorial Operators ◽  
Fractional Relaxation ◽  
Asymptotically Almost Periodic

We analyze asymptotically almost periodic solutions for a class of (semilinear) fractional relaxation inclusions with Stepanov almost periodic coefficients. As auxiliary tools, we use subordination principles, fixed point theorems and the well known results on the generation of infinitely differentiable degenerate semigroups with removable singularities at zero. Our results are well illustrated and seem to be not considered elsewhere even for fractional relaxation equations with almost sectorial operators.

scholarly journals Global Stability of Positive Periodic Solutions and Almost Periodic Solutions for a Discrete Competitive System

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Heping Ma ◽  
Jianguo Gao ◽  
Lingling Xie
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Periodic Solutions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Positive Periodic Solutions ◽  
Competitive System ◽  
Competitive Model ◽  
Uniformly Asymptotic Stability ◽  
Positive Almost Periodic Solutions

A discrete two-species competitive model is investigated. By using some preliminary lemmas and constructing a Lyapunov function, the existence and uniformly asymptotic stability of positive almost periodic solutions of the system are derived. In addition, an example and numerical simulations are presented to illustrate and substantiate the results of this paper.

Existence of almost periodic solutions for fractional impulsive neutral stochastic differential equations with infinite delay

2019 ◽  
Vol 20 (01) ◽  
pp. 2050003
Author(s):  
Xiao Ma ◽  
Xiao-Bao Shu ◽  
Jianzhong Mao
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Calculus ◽  
Stochastic Differential Equations ◽  
Periodic Solutions ◽  
Infinite Delay ◽  
Almost Periodic Solutions ◽  
Almost Periodic

In this paper, we investigate the existence of almost periodic solutions for fractional impulsive neutral stochastic differential equations with infinite delay in Hilbert space. The main conclusion is obtained by using fractional calculus, operator semigroup and fixed point theorem. In the end, we give an example to illustrate our main results.

scholarly journals Almost Periodic Solutions for Second Order Dynamic Equations on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yan Wang ◽  
Lan Li
Keyword(s):  
Fixed Point ◽  
Periodic Solutions ◽  
Time Scales ◽  
Existence And Uniqueness ◽  
Second Order ◽  
Almost Periodic Functions ◽  
Dynamic Equations ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Periodic Functions

We firstly introduce the concept and the properties ofCmalmost periodic functions on time scales, which generalizes the concept of almost periodic functions on time scales and the concept ofC(n)-almost periodic functions. Secondly, we consider the existence and uniqueness of almost periodic solutions for second order dynamic equations on time scales by Schauder’s fixed point theorem and contracting mapping principle. At last, we obtain alternative theorems for second order dynamic equations on time scales.

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