scholarly journals The Permanence and Extinction of the Single Species with Contraception Control and Feedback Controls

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Qiuying Li ◽  
Fengqin Zhang ◽  
Xiaomei Feng ◽  
Wenjuan Wang ◽  
Kai Wang
Keyword(s):  
Population Size ◽  
Population Control ◽  
Sufficient Conditions ◽  
Single Species ◽  
Feedback Controls ◽  
Wildlife Species ◽  
Contraception Control ◽  
Sterility Control

Population control has become a major problem in many wildlife species. Sterility control through contraception has been proposed as a method for reducing population size. In this paper, the single species with sterility control and feedback controls is considered. Sufficient conditions are obtained for the permanence and extinction of the system. The results show that the feedback controls do not influence the permanence of the species.

scholarly journals Survival analysis of a stochastic delay single-species system in polluted environment with psychological effect and pulse toxicant input

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiangjun Dai ◽  
Suli Wang ◽  
Weizhi Xiong ◽  
Ni Li
Keyword(s):  
Sufficient Conditions ◽  
Single Species ◽  
Threshold Value ◽  
Psychological Effect ◽  
Polluted Environment ◽  
Population System ◽  
Stochastic Delay ◽  
Species Population ◽  
The Mean ◽  
Single Species Population

Abstract We propose and study a stochastic delay single-species population system in polluted environment with psychological effect and pulse toxicant input. We establish sufficient conditions for the extinction, nonpersistence in the mean, weak persistence, and strong persistence of the single-species population and obtain the threshold value between extinction and weak persistence. Finally, we confirm the efficiency of the main results by numerical simulations.

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.

Stabilizing Feedback Controls for Nonlinear Hamiltonian Systems and Nonconservative Bilinear Systems in Elasticity

1982 ◽  
Vol 104 (1) ◽  
pp. 27-32 ◽  
Author(s):  
S. N. Singh
Keyword(s):  
Asymptotic Stability ◽  
Hamiltonian Systems ◽  
Attitude Control ◽  
Sufficient Conditions ◽  
Bilinear Systems ◽  
Feedback Controls ◽  
Control Laws ◽  
Nonlinear Maps ◽  
The Stability ◽  
Necessary And Sufficient

Using the invariance principle of LaSalle [1], sufficient conditions for the existence of linear and nonlinear control laws for local and global asymptotic stability of nonlinear Hamiltonian systems are derived. An instability theorem is also presented which identifies the control laws from the given class which cannot achieve asymptotic stability. Some of the stability results are based on certain results for the univalence of nonlinear maps. A similar approach for the stabilization of bilinear systems which include nonconservative systems in elasticity is used and a necessary and sufficient condition for stabilization is obtained. An application to attitude control of a gyrostat Satellite is presented.

Global dissipativity of stochastic Lotka–Volterra system with feedback controls

2017 ◽  
Vol 10 (02) ◽  
pp. 1750022 ◽  
Author(s):  
Qimin Zhang ◽  
Xinjing Zhang ◽  
Hongfu Yang
Keyword(s):  
Linear Matrix Inequalities ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Jensen Inequality ◽  
Linear Matrix ◽  
Mean Square ◽  
Matrix Inequalities ◽  
Volterra System ◽  
Feedback Controls ◽  
The Mean

In this paper, a class of stochastic Lotka–Volterra system with feedback controls is considered. The purpose is to establish some criteria to ensure the system is globally dissipative in the mean square. By constructing suitable Lyapunov functions as well as combining with Jensen inequality and It[Formula: see text] formula, the sufficient conditions are established and they are expressed in terms of the feasibility to a couple linear matrix inequalities (LMIs). Finally, the main results are illustrated by examples.

Population Control: Natural versus Human

1993 ◽  
Author(s):  
Garrett Hardin
Keyword(s):  
Exponential Growth ◽  
Homo Sapiens ◽  
Population Control ◽  
Single Species ◽  
The Self ◽  
Human Beings ◽  
The Gift ◽  
Functional Equivalent ◽  
Level Of Living ◽  
Over Time

Were we able to talk with other animals, it is extremely unlikely that we should hear them debating the problem of population control. They don't need to debate: nature solves the problem for them. And what is the problem? Simply this: to keep a successful species from being too successful. To keep it from eating itself out of house and home. And the solution? Simply predation and disease, which play the role that human beings might label "providence." As far as the written record reveals, no one recognized the self-elimination of a species as a potential problem for animals until the danger had become suspected among human beings. One of the earliest descriptions of this population problem for other animals was given by the Reverend Joseph Townsend, an English geologist. His key contribution was published in 1786, twelve years before Malthus's celebrated essay (Box 25-1). Townsend was dependent upon others for the outline of his story, and there is some question as to whether the details are historically correct. But the thrust of the story must be true: a single species (goats, in this case) exploiting a resource (plants) cannot, by itself, maintain a stable equilibrium at a comfortable level of living. The animals will either die after eating up all the food, or their numbers will fluctuate painfully. (Details differ, depending on the species and the environment.) Stability and prosperity require that the gift of exponential growth be opposed by some sort of countervailing force (predatory dogs, in Townsend's example). However deplorable predators may be for individuals who happen to be captured and eaten, for the prey population as a whole predators are (over time) a blessing. With millions of different species of animals there are many different particular explanations of how they manage to persist for thousands or millions of years. The species we are most interested in is, of course, Homo sapiens. A meditation on Townsend's account led to a challenging set of questions. "If all this great earth be no more than the Island of Juan Fernandes, and if we are the goats, how can we live "the good life" without a functional equivalent of the dogs? Must we create and sustain our own dogs? Can we do so, consciously? And if we can, what manner of beast will they be?"

The Wright–Fisher model with varying selection

1986 ◽  
Vol 23 (02) ◽  
pp. 504-508
Author(s):  
N. C. Weber
Keyword(s):  
Population Growth ◽  
Population Size ◽  
Sufficient Conditions ◽  
Selective Advantage ◽  
Fisher Model ◽  
Ultimate Homozygosity ◽  
Varying Population

The Wright–Fisher model with varying population size is examined in the case where the selective advantage varies from generation to generation. Models are considered where the selective advantage is not always in favour of a particular genotype. Sufficient conditions in terms of the selection coefficients and the population growth are given to ensure ultimate homozygosity.

scholarly journals Positive Periodic Solutions of Cooperative Systems with Delays and Feedback Controls

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Tursuneli Niyaz ◽  
Ahmadjan Muhammadhaji
Keyword(s):  
Periodic Solutions ◽  
Continuous Time ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Positive Periodic Solutions ◽  
Feedback Controls ◽  
Volterra Systems

This paper studies a class of periodicnspecies cooperative Lotka-Volterra systems with continuous time delays and feedback controls. Based on the continuation theorem of the coincidence degree theory developed by Gaines and Mawhin, some new sufficient conditions on the existence of positive periodic solutions are established.

Permanence and extinction of a single species model in polluted environment

2020 ◽  
Vol 13 (04) ◽  
pp. 2050031
Author(s):  
Jiandong Zhao ◽  
Tonghua Zhang
Keyword(s):  
Sufficient Conditions ◽  
Single Species ◽  
Logistic Equation ◽  
Polluted Environment ◽  
Math Model ◽  
Generalized Logistic Equation ◽  
Appl Math ◽  
Single Species Model

Under the assumption that the growth of the population satisfies the generalized logistic equation, a new single species model in polluted environment is proposed in this work. Sufficient conditions for permanence and extinction of the species in the model are given respectively. It is shown that our model and the results are improvements of those in He and Wang [Appl. Math. Model. 31 (2007) 2227–2238].

Asymptotic behavior of near-critical multitype branching processes

1991 ◽  
Vol 28 (03) ◽  
pp. 512-519 ◽  
Author(s):  
Fima C. Klebaner
Keyword(s):  
Asymptotic Behavior ◽  
Population Size ◽  
Discrete Time ◽  
Growth Rates ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Limiting Distribution ◽  
Size Dependent ◽  
Generalized Gamma ◽  
Multitype Branching Processes

Sufficient conditions for survival and extinction of multitype population-size-dependent branching processes in discrete time are obtained. Growth rates are determined on the set of divergence to infinity. The limiting distribution of a properly normalized process can be generalized gamma, normal or degenerate.

scholarly journals Permanence of a Single Species System with Distributed Time Delay and Feedback Control

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yali Shen ◽  
Fengqin Zhang ◽  
Kai Wang
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Single Species ◽  
Feedback Controls ◽  
Distributed Time Delay

We study the permanence of a classofsingle species system with distributed time delay and feedback controls. General criteria on permanence are established in this paper. A very important fact is found in our results; that is, the feedback control is harmless to the permanence of species.

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