scholarly journals Positive periodic solution for a nonlinear neutral delay population equation with feedback control

2014 ◽  
Vol 07 (03) ◽  
pp. 218-228 ◽  
Author(s):  
Payam Nasertayoob ◽  
S. Mansour Vaezpour
Keyword(s):  
Periodic Solution ◽  
Feedback Control ◽  
Positive Periodic Solution ◽  
Neutral Delay ◽  
Population Equation

scholarly journals A New Existence Theory for Positive Periodic Solutions to a Class of Neutral Delay Model with Feedback Control and Impulse

2013 ◽  
Vol 2013 ◽  
pp. 1-18
Author(s):  
Zhenguo Luo ◽  
Jianhua Huang ◽  
Binxiang Dai
Keyword(s):  
Feedback Control ◽  
Positive Periodic Solution ◽  
Existence Theory ◽  
Delay Model ◽  
Positive Periodic Solutions ◽  
Neutral Delay ◽  
Mawhin’S Continuation Theorem ◽  
Analysis Techniques ◽  
Special Cases ◽  
Competitive Model

We acquire some sufficient and realistic conditions for the existence of positive periodic solution of a general neutral impulsive n-species competitive model with feedback control by applying some analysis techniques and a new existence theorem, which is different from Gaines and Mawhin's continuation theorem and abstract continuation theory for k-set contraction. As applications, we also examine some special cases, which have been studied extensively in the literature, some known results are improved and generalized.

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 the Uniqueness and Dependence of Positive Periodic Solutions for Delay Differential Systems with Feedback Control

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Haitao Li ◽  
Yansheng Liu
Keyword(s):  
Periodic Solution ◽  
Feedback Control ◽  
Operator Theory ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Mixed Monotone Operator ◽  
Differential Systems ◽  
Delay Differential Systems ◽  
Monotone Operator Theory ◽  
Delay Differential

This paper investigates a class of delay differential systems with feedback control. Sufficient conditions are obtained for the existence and uniqueness of the positive periodic solution by utilizing some results from the mixed monotone operator theory. Meanwhile, the dependence of the positive periodic solution on the parameterλis also studied. Finally, an example together with numerical simulations is worked out to illustrate the main results.

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].

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