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 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 Dynamic Analysis of a Model for Spruce Budworm Populations with Delay

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Ahmadjan Muhammadhaji ◽  
Azhar Halik
Keyword(s):  
Numerical Simulation ◽  
Dynamic Analysis ◽  
Periodic Solutions ◽  
Population Model ◽  
Lyapunov Functional ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Spruce Budworm ◽  
Positive Periodic Solutions ◽  
Inequality Techniques

A class of delayed spruce budworm population model is considered. Compared with previous studies, both autonomous and nonautonomous delayed spruce budworm population models are considered. By using the inequality techniques, continuation theorem, and the construction of suitable Lyapunov functional, we establish a set of easily verifiable sufficient conditions on the permanence, existence, and global attractivity of positive periodic solutions for the considered system. Finally, an example and its numerical simulation are given to illustrate our main results.

scholarly journals Periodicity and positivity in nonlinear neutral integro-dynamic equations with variable delay

Mathematica ◽  
2020 ◽  
Vol 62 (85) (2) ◽  
pp. 117-132
Author(s):  
Malik Belaid ◽  
Abdelouaheb Ardjouni ◽  
Ahcene Djoudi
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Dynamic Equations ◽  
Variable Delay ◽  
Positive Periodic Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Completely Continuous ◽  
Continuous Map ◽  
Uniqueness Results

Let T be a periodic time scale. We use Krasnoselskii's fixed point theorem for a sum of two operators to show new results on the existence of periodic and positive periodic solutions of a nonlinear neutral integro-dynamic equation with variable delay. We invert this equation to construct a sum of a contraction and a completely continuous map which is suitable for applying Krasnoselskii's theorem. The uniqueness results of this equation are studied by the contraction mapping principle.

scholarly journals EXISTENCE AND STABILITY ANALYSIS OF SOLUTIONS FOR FRACTIONAL LANGEVIN EQUATION WITH NONLOCAL INTEGRAL AND ANTI-PERIODIC-TYPE BOUNDARY CONDITIONS

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040006 ◽  
Author(s):  
AMITA DEVI ◽  
ANOOP KUMAR ◽  
THABET ABDELJAWAD ◽  
AZIZ KHAN
Keyword(s):  
Boundary Conditions ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Banach Contraction ◽  
Existence And Stability ◽  
Fractional Differential ◽  
Type Boundary ◽  
Banach Contraction Mapping Principle ◽  
Banach Contraction Mapping

In this paper, we deal with the existence and uniqueness (EU) of solutions for nonlinear Langevin fractional differential equations (FDE) having fractional derivative of different orders with nonlocal integral and anti-periodic-type boundary conditions. Also, we investigate the Hyres–Ulam (HU) stability of solutions. The existence result is derived by applying Krasnoselskii’s fixed point theorem and the uniqueness of result is established by applying Banach contraction mapping principle. An example is offered to ensure the validity of our obtained results.

PERIODICITY IN AN STAGE-STRUCTURED THREE-SPECIES PREDATOR–PREY SYSTEM WITH BEDDINGTON–DEANGELIS AND HOLLINF IV FUNCTIONAL RESPONSE

2012 ◽  
Vol 05 (02) ◽  
pp. 1250031
Author(s):  
Changjin Xu ◽  
Maoxin Liao
Keyword(s):  
Functional Response ◽  
Lyapunov Functional ◽  
Global Attractivity ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solution ◽  
Sufficient Condition ◽  
Positive Periodic Solutions ◽  
Predator Prey ◽  
Prey System

In this paper, by using the continuation theorem of coincidence degree theory, a sufficient condition of existence of positive periodic solutions is obtained for an stage-structured three-species predator–prey system with Beddington–DeAngelis and Holling IV functional response. By constructing a suitable Lyapunov functional, the uniqueness and global attractivity of the positive periodic solution are presented. Our result is a good complement to the earlier publications.

scholarly journals Global Attractivity of Positive Periodic Solutions of Delay Differential Equations with Feedback Control

2007 ◽  
Vol 2007 ◽  
pp. 1-11 ◽  
Author(s):  
Zhi-Long Jin
Keyword(s):  
Feedback Control ◽  
Periodic Solutions ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Upper And Lower Bounds ◽  
Positive Periodic Solutions ◽  
Liapunov Functionals ◽  
Delay Differential System ◽  
Several Delays ◽  
Delay Differential

By constructing suitable Liapunov functionals and estimating uniform upper and lower bounds of solutions, sufficient conditions are obtained for the global attractivity of positive periodic solutions of the delay differential system with feedback controldy/dt=y(t)F(t,y(t−τ1(t)),…,y(t−τn(t)),u(t−δ(t))),du/dt=−η(t)u(t)+a(t)y(t−σ(t)). When these results are applied to the periodic logistic equation with several delays and feedback control, some new results are obtained.

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