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

2011 ◽  
Vol 217 (19) ◽  
pp. 7692-7702 ◽  
Author(s):  
Rui Wang ◽  
Xiaosheng Zhang
Keyword(s):  
Periodic Solution ◽  
Feedback Control ◽  
Population Model ◽  
Positive Periodic Solution

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 Existence and Global Attractivity of Positive Periodic Solutions for The Neutral Multidelay Logarithmic Population Model with Impulse

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Zhenguo Luo ◽  
Jianhua Huang ◽  
Liping Luo ◽  
Binxiang Dai
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Population Model ◽  
Global Attractivity ◽  
Positive Periodic Solution ◽  
Positive Periodic Solutions ◽  
Contractive Operator ◽  
Inequality Techniques

Suffiicient and realistic conditions are established in this paper for the existence and global attractivity of a positive periodic solution to the neutral multidelay logarithmic population model with impulse by using the theory of abstract continuous theorem of k-set contractive operator and some inequality techniques. The results improve and generalize the known ones in Li 1999, Lu and Ge 2004, Y. Luo and Z. G. Luo 2010, and Wang et al. 2009. As an application, we also give an example to illustrate the feasibility of our main results.

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 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.

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