Positive periodic solution of a neutral delay competition model with impulses

2005 ◽  
Vol 84 (11) ◽  
pp. 1103-1116 ◽  
Author(s):  
Hai-Feng Huo ◽  
Wan-Tong Li
Keyword(s):  
Periodic Solution ◽  
Positive Periodic Solution ◽  
Competition Model ◽  
Neutral Delay

scholarly journals Positive Periodic Solution for the Generalized Neutral Differential Equation with Multiple Delays and Impulse

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Zhenguo Luo ◽  
Liping Luo ◽  
Yunhui Zeng
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Fixed Point ◽  
Positive Periodic Solution ◽  
Multiple Delays ◽  
Neutral Delay ◽  
Mawhin’S Continuation Theorem ◽  
Volterra Models ◽  
Functional Differential ◽  
New Criteria

By using a fixed point theorem of strict-set-contraction, which is different from Gaines and Mawhin's continuation theorem and abstract continuation theory fork-set contraction, we established some new criteria for the existence of positive periodic solution of the following generalized neutral delay functional differential equation with impulse:x'(t)=x(t)[a(t)-f(t,x(t),x(t-τ1(t,x(t))),…,x(t-τn(t,x(t))),x'(t-γ1(t,x(t))),…,x'(t-γm(t,x(t))))],  t≠tk,  k∈Z+;  x(tk+)=x(tk-)+θk(x(tk)),  k∈Z+. As applications of our results, we also give some applications to several Lotka-Volterra models and new results are obtained.

scholarly journals On a periodic neutral logistic equation

1991 ◽  
Vol 33 (3) ◽  
pp. 281-286 ◽  
Author(s):  
K. Gopalsamy ◽  
Xue-Zhong He ◽  
Lizhi Wen
Keyword(s):  
Periodic Solution ◽  
Positive Integer ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Logistic Equation ◽  
Periodic Functions ◽  
Neutral Delay ◽  
Periodic Delay ◽  
Image Position ◽  
Delay Logistic Equation

The oscillatory and asymptotic behaviour of the positive solutions of the autonomous neutral delay logistic equationwith r, c, T, K ∈ (0, ∞) has been recently investigated in [2]. More recently the dynamics of the periodic delay logistic equationin which r, K are periodic functions of period τ and m is a positive integer is considered in [6]. The purpose of the following analysis is to obtain sufficient conditions for the existence and linear asymptotic stability of a positive periodic solution of a periodic neutral delay logistic equationin which Ṅ denotes and r, K, c are positive continuous periodic functions of period τ at and m is a positive integer. For the origin and biological relevance of (1.3) we refer to [2].

scholarly journals Investigation on dynamics of an impulsive predator–prey system with generalized Holling type IV functional response and anti-predator behavior

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sekson Sirisubtawee ◽  
Nattawut Khansai ◽  
Akapak Charoenloedmongkhon
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Impulsive Control ◽  
Positive Periodic Solution ◽  
Existence Condition ◽  
Predator Prey ◽  
Type Iv ◽  
Prey System ◽  
Existence And Stability ◽  
Predator Behavior

AbstractIn the present article, we propose and analyze a new mathematical model for a predator–prey system including the following terms: a Monod–Haldane functional response (a generalized Holling type IV), a term describing the anti-predator behavior of prey populations and one for an impulsive control strategy. In particular, we establish the existence condition under which the system has a locally asymptotically stable prey-eradication periodic solution. Violating such a condition, the system turns out to be permanent. Employing bifurcation theory, some conditions, under which the existence and stability of a positive periodic solution of the system occur but its prey-eradication periodic solution becomes unstable, are provided. Furthermore, numerical simulations for the proposed model are given to confirm the obtained theoretical results.

scholarly journals An exact expression of positive periodic solution for a first-order singular equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yun Xin ◽  
Xiaoxiao Cui ◽  
Jie Liu
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Lower Bounds ◽  
Topological Degree ◽  
Order Differential Equation ◽  
Positive Periodic Solution ◽  
Exact Expression ◽  
Upper And Lower Bounds ◽  
Singular Equation ◽  
First Order

Abstract The main purpose of this paper is to obtain an exact expression of the positive periodic solution for a first-order differential equation with attractive and repulsive singularities. Moreover, we prove the existence of at least one positive periodic solution for this equation with an indefinite singularity by applications of topological degree theorem, and give the upper and lower bounds of the positive periodic solution.

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