scholarly journals Dynamics for a discrete competition and cooperation model of two enterprises with multiple delays and feedback controls

2017 ◽  
Vol 15 (1) ◽  
pp. 218-232
Author(s):  
Lin Lu ◽  
Yi Lian ◽  
Chaoling Li
Keyword(s):  
Sufficient Conditions ◽  
Suitable Condition ◽  
Multiple Delays ◽  
Stable Periodic Solution ◽  
Feedback Controls ◽  
Competition And Cooperation ◽  
Inequality Theory ◽  
Stable Periodic ◽  
Cooperation Model ◽  
The Difference

Abstract This paper is concerned with a competition and cooperation model of two enterprises with multiple delays and feedback controls. With the aid of the difference inequality theory, we have obtained some sufficient conditions which guarantee the permanence of the model. Under a suitable condition, we prove that the system has global stable periodic solution. The paper ends with brief conclusions.

scholarly journals Permanence in a Discrete Mutualism Model with Infinite Deviating Arguments and Feedback Controls

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Changjin Xu ◽  
Yusen Wu
Keyword(s):  
Sufficient Conditions ◽  
Feedback Controls ◽  
Difference Inequality ◽  
Deviating Arguments ◽  
Inequality Theory ◽  
The Difference ◽  
Mutualism Model

We propose and deal with a discrete mutualism model with infinite deviating arguments and feedback controls. Sufficient conditions which guarantee the permanence of the system are obtained by using the difference inequality theory. The paper ends with brief conclusions.

scholarly journals Permanence and Almost Periodic Solution for an Enterprise Cluster Model Based on Ecology Theory with Feedback Controls on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Yuanhong Zhi ◽  
Zunling Ding ◽  
Yongkun Li
Keyword(s):  
Periodic Solution ◽  
Time Scales ◽  
Cluster Model ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Feedback Controls ◽  
Competition And Cooperation ◽  
Enterprise Cluster

We present a model with feedback controls based on ecology theory, which effectively describes the competition and cooperation of enterprise cluster in real economic environments. Applying the comparison theorem of dynamic equations on time scales and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and the existence of uniformly asymptotically stable almost periodic solution of the system are obtained.

scholarly journals Global asymptotic stability in a periodic Lotka-Volterra system

1985 ◽  
Vol 27 (1) ◽  
pp. 66-72 ◽  
Author(s):  
K. Gopalsamy
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Stable Periodic Solution ◽  
Volterra System ◽  
Periodic Coefficients ◽  
Globally Asymptotically Stable ◽  
Stable Periodic

AbstractA set of easily verifiable sufficient conditions are obtained for the existence of a globally asymptotically stable periodic solution in a Lotka-Volterra system with periodic coefficients.

scholarly journals Dynamic Behaviors of a Discrete Periodic Predator-Prey-Mutualist System

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Liya Yang ◽  
Xiangdong Xie ◽  
Fengde Chen
Keyword(s):  
Periodic Solution ◽  
Numerical Simulations ◽  
Sufficient Conditions ◽  
Cooperative Effect ◽  
Stable Periodic Solution ◽  
Predator Species ◽  
Predator Prey ◽  
Stable Periodic ◽  
Extinction Property ◽  
Globally Stable

A nonautonomous discrete predator-prey-mutualist system is proposed and studied in this paper. Sufficient conditions which ensure the permanence and existence of a unique globally stable periodic solution are obtained. We also investigate the extinction property of the predator species; our results indicate that if the cooperative effect between the prey and mutualist species is large enough, then the predator species will be driven to extinction due to the lack of enough food. Two examples together with numerical simulations show the feasibility of the main results.

scholarly journals Dynamic Behavior of Positive Solutions for a Leslie Predator-Prey System with Mutual Interference and Feedback Controls

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Cong Zhang ◽  
Nan-jing Huang ◽  
Chuan-xian Deng
Keyword(s):  
Global Attractivity ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Mutual Interference ◽  
Periodic Case ◽  
Feedback Controls ◽  
Predator Prey ◽  
Prey System ◽  
Inequality Theory ◽  
Nonautonomous Case

We consider a Leslie predator-prey system with mutual interference and feedback controls. For general nonautonomous case, by using differential inequality theory and constructing a suitable Lyapunov functional, we obtain some sufficient conditions which guarantee the permanence and the global attractivity of the system. For the periodic case, we obtain some sufficient conditions which guarantee the existence, uniqueness, and stability of a positive periodic solution.

scholarly journals Exchange of equilibria in two species Lotka-Volterra competition models

1982 ◽  
Vol 24 (2) ◽  
pp. 160-170 ◽  
Author(s):  
K. Gopalsamy
Keyword(s):  
Periodic Solution ◽  
Sufficient Conditions ◽  
System Of Equations ◽  
Species Competition ◽  
Asymptotically Stable ◽  
Stable Periodic Solution ◽  
Periodic Functions ◽  
Competition System ◽  
Competition Models ◽  
Stable Periodic

AbstractSufficient conditions are obtained for the existence of a unique asymptotically stable periodic solution for the Lotka-Volterra two species competition system of equations when the intrinsic growth rates are periodic functions of time.

scholarly journals Complete Controllability Conditions for Linear Singularly Perturbed Time-Invariant Systems with Multiple Delays via Chang-Type Transformation

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 71 ◽  
Author(s):  
Olga Tsekhan
Keyword(s):  
Sufficient Conditions ◽  
Singularly Perturbed ◽  
Degenerate System ◽  
Multiple Delays ◽  
Complete Controllability ◽  
Singularly Perturbed System ◽  
System With Delay ◽  
Perturbed System ◽  
Time Invariant ◽  
Controllability Conditions

The problem of complete controllability of a linear time-invariant singularly-perturbed system with multiple commensurate non-small delays in the slow state variables is considered. An approach to the time-scale separation of the original singularly-perturbed system by means of Chang-type non-degenerate transformation, generalized for the system with delay, is used. Sufficient conditions for complete controllability of the singularly-perturbed system with delay are obtained. The conditions do not depend on a singularity parameter and are valid for all its sufficiently small values. The conditions have a parametric rank form and are expressed in terms of the controllability conditions of two systems of a lower dimension than the original one: the degenerate system and the boundary layer system.

scholarly journals Stochastic Comparisons of Some Distances between Random Variables

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 981
Author(s):  
Patricia Ortega-Jiménez ◽  
Miguel A. Sordo ◽  
Alfonso Suárez-Llorens
Keyword(s):  
Financial Risk ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Stochastic Ordering ◽  
Random Variable ◽  
Distribution Functions ◽  
Stochastic Comparisons ◽  
Stochastic Orderings ◽  
Absolute Value ◽  
The Difference

The aim of this paper is twofold. First, we show that the expectation of the absolute value of the difference between two copies, not necessarily independent, of a random variable is a measure of its variability in the sense of Bickel and Lehmann (1979). Moreover, if the two copies are negatively dependent through stochastic ordering, this measure is subadditive. The second purpose of this paper is to provide sufficient conditions for comparing several distances between pairs of random variables (with possibly different distribution functions) in terms of various stochastic orderings. Applications in actuarial and financial risk management are given.

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