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 Existence and Stability of Positive Periodic Solutions for a Neutral Multispecies Logarithmic Population Model with Feedback Control and Impulse

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Zhenguo Luo ◽  
Liping Luo
Keyword(s):  
Feedback Control ◽  
Population Model ◽  
Contraction Mapping ◽  
Global Attractivity ◽  
Positive Periodic Solution ◽  
Contraction Mapping Principle ◽  
Positive Periodic Solutions ◽  
Special Cases ◽  
Existence And Stability ◽  
Inequality Techniques

We investigate a neutral multispecies logarithmic population model with feedback control and impulse. By applying the contraction mapping principle and some inequality techniques, a set of easily applicable criteria for the existence, uniqueness, and global attractivity of positive periodic solution are established. The conditions we obtained are weaker than the previously known ones and can be easily reduced to several special cases. We also give an example to illustrate the applicability of our results.

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 Positive periodic solution for inertial neural networks with time-varying delays

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Feng Duan ◽  
Bo Du
Keyword(s):  
Neural Networks ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Functional Method ◽  
Time Varying ◽  
Positive Periodic Solutions ◽  
Mawhin’S Continuation Theorem ◽  
Existence And Stability ◽  
Inertial Neural Networks

AbstractIn this paper the problems of the existence and stability of positive periodic solutions of inertial neural networks with time-varying delays are discussed by the use of Mawhin’s continuation theorem and Lyapunov functional method. Some sufficient conditions are obtained for guaranteeing the existence and stability of positive periodic solutions of the considered system. Finally, a numerical example is given to illustrate the effectiveness of the obtained results.

scholarly journals Two Positive Periodic Solutions for a Neutral Delay Model of Single-Species Population Growth with Harvesting

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Hui Fang
Keyword(s):  
Population Growth ◽  
Periodic Solutions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Single Species ◽  
Delay Model ◽  
Positive Periodic Solutions ◽  
Neutral Delay ◽  
Species Population ◽  
Single Species Population

By coincidence degree theory fork-set-contractive mapping, this paper establishes a new criterion for the existence of at least two positive periodic solutions for a neutral delay model of single-species population growth with harvesting. An example is given to illustrate the effectiveness of the result.

scholarly journals Existence of periodic positive solutions to nonlinear Lotka-Volterra competition systems

2020 ◽  
Vol 40 (3) ◽  
pp. 341-360
Author(s):  
Mimia Benhadri ◽  
Tomás Caraballo ◽  
Halim Zeghdoudi
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Main Tool ◽  
Positive Periodic Solution ◽  
Positive Periodic Solutions ◽  
Deviating Arguments ◽  
Competition System ◽  
Special Cases ◽  
Krasnoselskii Fixed Point Theorem

We investigate the existence of positive periodic solutions of a nonlinear Lotka-Volterra competition system with deviating arguments. The main tool we use to obtain our result is the Krasnoselskii fixed point theorem. In particular, this paper improves important and interesting work [X.H. Tang, X. Zhou, On positive periodic solution of Lotka-Volterra competition systems with deviating arguments, Proc. Amer. Math. Soc. 134 (2006), 2967-2974]. Moreover, as an application, we also exhibit some special cases of the system, which have been studied extensively in the literature.

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