Positive periodic solution for a neutral Logarithmic population model with feedback control

In this paper, a neutral delay Logarithmic population model with feedback control is studied. By using the abstract continuous theorem of k-set contractive operator, some new results on the existence of the positive periodic solution are obtained; after that, by constructing a suitable Lyapunov functional, a set of easily applicable criteria is established for the global asymptotically stability of the positive periodic solution.     

Existence of positive periodic solutions for neutral multi-delay logarithmic population model

In the paper, a new result is obtained for the existence of positive periodic solutions to a neutral multi-delay logarithmic population model. Our analysis mainly relies on an abstract continuous theorem of k-set contractive operator. We also give an example to illustrate the applicability of our results.     

Existence and exponential stability of almost periodic solutions for a neutral multi-species Logarithmic population model

In this paper, we study the almost periodic solution for a neutral multi-species Logarithmic population model. By employing Banach’s fixed point theorem and using differential inequality technique, we present some sufficient conditions ensuring the existence, uniqueness and globally exponential stability of almost periodic solution for the model. The results obtained extend and improve the earlier publications. Finally, two examples are provided to show the correctness of our analysis.     

Existence of periodic solutions for neutral type cellular neural networks with delays

In this paper, by using the theory of abstract continuation theorem of k contractive operator, we study the existence of periodic solutions for neutral type cellular neural networks with delays.     

Positive periodic solutions for a class of nonlinear delay equations

Applying the theory of topological degree, sufficient and realistic conditions are obtained for the existence of positive periodic solutions of a class of neutral delays equation. From those conditions, an algebraic criterion of existence for a more general neutral Lotka–Volterra equation with several delays is obtained, which extends and improves the previous results. In addition, this method is of great interest in many applications such as biomathematics.     

Existence of positive periodic solutions for a neutral population model with delays and impulse

In this paper, by using the theory of abstract continuous theorem of k$k$-set contractive operator and some analysis techniques, we obtain some sufficient conditions for the existence of positive periodic solutions for a neutral population model with delays and impulse.     

一类多滞量周期扰动非线性系统的周期解

研究一类具有多个滞量的周期扰动非线性系统的T周期解.利用拓扑度的方法得到了系统存在T周期解的充分条件.作为应用,证明了具有滞后的单种群对数模型在一定条件下存在正周期解.     

New results of existence and stability of periodic solution for a delay multispecies Logarithmic population model

In this Letter, for a general class of delayed periodic multispecies Logarithmic population model, we prove some new results on the existence of positive periodic solutions by contraction principle. The global exponential stability of positive periodic solutions is discussed further, and conditions for exponential convergence are given. The conditions we obtained are weaker than the previously known ones and can be easily reduced to several special cases.     

Existence of periodic solutions in neutral state-dependent delays equations and models

Sufficient conditions are obtained for the existence of positive periodic solutions of neutral equations with state-dependent delays. The proof is based on the theory of coincidence degree. The existence results are applied to equations of population dynamics.     

Positive periodic solutions for a neutral impulsive delayed Lotka–Volterra competition system with the effect of toxic substance

Based on the coincidence degree theory and its related continuation theorem as well as some a priori estimates, we explore the existence of periodic solutions with strictly positive components of a neutral delayed Lotka–Volterra competitive system with impulse. Easily verifiable sufficient criteria are established for the existence of positive periodic solution for the neutral impulsive system. When the results reduce to neutral system without impulse, they generalize the results in Yang and Cao [Positive periodic solutions of neutral Lotka–Volterra system with periodic delays, Appl. Math. Comput. 149 (2004) 661–687].     

Periodic solution of neutral Lotka-Volterra system with periodic delays

A nonautonomous n-species Lotka-Volterra system with neutral delays is investigated. A set of verifiable sufficient conditions is derived for the existence of at least one strictly positive periodic solution of this Lotka-Volterra system by applying an existence theorem and some analysis techniques, where the assumptions of the existence theorem are different from that of Gaines and Mawhin's continuation theorem [R.E. Gaines, J.L. Mawhin, Coincidence Degree and Nonlinear Differential Equations, Springer-Verlag, Berlin, 1977] and that of abstract continuation theory for k-set contraction [W. Petryshyn, Z. Yu, Existence theorem for periodic solutions of higher order nonlinear periodic boundary value problems, Nonlinear Anal. 6 (1982) 943-969]. Moreover, a problem proposed by Freedman and Wu [H.I. Freedman, J. Wu, Periodic solution of single species models with periodic delay, SIAM J. Math. Anal. 23 (1992) 689-701] is answered.     

Positive almost periodic solution for a class of Nicholson’s blowflies model with multiple time-varying delays

In this paper, we study the existence and exponential convergence of positive almost periodic solutions for the generalized Nicholson’s blowflies model with multiple time-varying delays. Under proper conditions, we establish some criteria to ensure that the solutions of this model converge locally exponentially to a positive almost periodic solution. Moreover, we give some examples to illustrate our main results.     

Hopf bifurcation analysis in a multiple delayed innovation diffusion model with Holling II functional response

A nonlinear mathematical model with Holling II functional response describing the dynamics of nonadopter and adopters population in a stage structured innovation diffusion model, which incorporates the evaluation stage (multiple delays), is proposed. Firstly, we study the stability and the existence of periodic solutions via Hopf bifurcation with respect to both delays at the positive equilibrium by analyzing the distribution of the roots of the corresponding exponential characteristic equation obtained through the variational matrix. The direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined with the help of normal form theory and center manifold theorem. Meanwhile, various cases are discussed to examine the effect of different delays on the stability of delayed innovation diffusion system and are also established numerically. It is also observed that the cumulative density of external influences has a significant role in developing maturity stage (adoption stage) in the system. Finally, numerical simulations are carried out to support and supplement the analytical findings.     

Positive periodic solution for a neutral delay competitive system

In this paper we study the existence of positive periodic solutions for a class of neutral type competitive system with delay. Applying the continuation theorem of coincidence degree theory, a general criteria on the existence of positive periodic solutions are established. Some the related results are generalized and improved. It is shown that the arguments delays have no effect on the existence positive periodic solution of system.     

带有脉冲和Holling-Ⅳ型功能反应函数的中立型捕食-食饵模型的周期解

该文研究一类带有中立型脉冲时滞和Holling-Ⅳ型功能反应函数的捕食-食饵模型.通过运用Mawhin迭合度理论和分析技巧,得到了捕食-食饵模型正周期解存在性的充分条件.     

Positive almost periodic solution for a class of Nicholson’s blowflies model with a linear harvesting term

In this paper, we study the problem of positive almost periodic solutions for the generalized Nicholson’s blowflies model with a linear harvesting term and multiple time-varying delays. By applying the fixed point theorem and the Lyapunov functional method, we establish some criteria to ensure that the solutions of this model converge locally exponentially to a positive almost periodic solution. Moreover, we give an example to illustrate our main results.     

Positive periodic solutions of nonautonomous delay competitive systems with weak Allee effect

This paper considers a nonautonomous Lotka–Volterra type multispecies competitive system with weak Allee effect and delays. The model has the intraspecific competition terms defined by sign changing functions which depend on population density monotonically and time periodically. An existence theorem of positive periodic solutions is established using the coincidence degree theory. Furthermore, for the case of constant delays, a sufficient condition for the positive periodic solution to be globally attractive is proved with the Lyapunov method so that the system attains permanence.     

Positive Periodic Solutions of a Class of Non-autonomous Single Species Population Model with Delays and Feedback Control

With the help of a continuation theorem based on Gaines and Mawhin＇s coincidence degree, several verifiable criteria are established for the global existence of positive periodic solutions of a class of non-autonomous single species population model with delays （both state-dependent delays and continuous delays） and feedback control. After that, by constructing a suitable Lyapunov functional, sufficient conditions which guarantee the existence of a unique globally asymptotic stable positive periodic solution of a kind of nonlinear feedback control ecosystem are obtained. Our results extend and improve the existing results, and have further applications in population dynamics.     

一个周期中立型对数种群模型

本文获得了周期中立型对数种群模型N(t)=N(t)(r(t)-α(t)log[N(t-σ)]-b(t)d/dtlog[N(t-r)])的周期正解的存在性及对所有正解的吸引性．     

The behavior of the solutions of periodic linear neutral delay difference equations

Some new asymptotic, nonoscillation and stability criteria for linear neutral delay difference equations with periodic coefficients and constant delays are given. The results are obtained via a positive root (with suitable properties) of an associated equation which is, in a sense, the corresponding characteristic equation.