PERSISTENCE, EXTINCTION AND STABILITY FOR NONLINEAR PLANKTON ALLELOPATHY MODEL WITH DELAYED NEGATIVE FEEDBACKS

2012 ◽  
Vol 05 (02) ◽  
pp. 1250027 ◽  
Author(s):  
YAN-PING LIU ◽  
ZHI-XUE LUO
Keyword(s):  
Numerical Simulations ◽  
Sufficient Conditions ◽  
Lyapunov Functionals ◽  
Analysis Method ◽  
Average Value ◽  
Competitive Systems ◽  
Comparison Argument ◽  
Negative Feedbacks ◽  
Plankton Allelopathy ◽  
The Stability

By the techniques of comparison argument and Lyapunov-like functionals, some criteria about persistence and extinction of the species are obtained. And then, with the help of constructing Lyapunov functionals and some new analysis method, sufficient conditions, provided with the form of average value of a function, to guarantee the stability of the system are derived. Finally, some examples together with their numerical simulations show the feasibility of these main results. Our conclusions are different from many existing forms for nonlinear competitive systems.

scholarly journals Global Stability and Oscillation of a Discrete Annual Plants Model

2010 ◽  
Vol 2010 ◽  
pp. 1-18
Author(s):  
S. H. Saker
Keyword(s):  
Fixed Point ◽  
Global Stability ◽  
Numerical Simulations ◽  
Positive Solutions ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Annual Plants ◽  
Discrete Delay ◽  
The Stability ◽  
Positive Fixed Point

The objective of this paper is to systematically study the stability and oscillation of the discrete delay annual plants model. In particular, we establish some sufficient conditions for global stability of the unique positive fixed point and establish an explicit sufficient condition for oscillation of the positive solutions about the fixed point. Some illustrative examples and numerical simulations are included to demonstrate the validity and applicability of the results.

String Exponential Stability With Mode Constraint of Stochastic Vehicle Following Systems

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Xiaohui Xu ◽  
Jiye Zhang ◽  
Lan Tang
Keyword(s):  
Exponential Stability ◽  
Sufficient Conditions ◽  
Original System ◽  
Analysis Method ◽  
Geometrical Analysis ◽  
Stochastic Disturbance ◽  
Infinite Dimensional ◽  
Vector Lyapunov Function ◽  
Lyapunov Function Method ◽  
The Stability

Associated with automatic vehicle following system is the problem of the stability of a platoon of vehicles. The stability with mode constraint is the property of damping disturbances as they travel away from the source in the system. In this paper, a class of infinite-dimensional vehicle longitudinal following system with stochastic disturbance is analyzed. By applying geometrical analysis method, a lemma for analyzing the stability of generalized vector comparison inequalities with respect to the original systems is established. With the help of the lemma, some sufficient conditions for assuring the string exponential stability with mode constraint of the original system are obtained by applying vector Lyapunov function method. The obtained conditions are less conservative than the existing ones. A numerical example is given to show the effectiveness of the established conditions.

PERMANENCE IN NONAUTONOMOUS DISCRETE LOTKA–VOLTERRA n-SPECIES COMPETITIVE SYSTEMS WITH PURE-DELAYS AND FEEDBACK CONTROLS

2013 ◽  
Vol 24 (07) ◽  
pp. 1350053 ◽  
Author(s):  
AHMADJAN MUHAMMADHAJI ◽  
ZHIDONG TENG ◽  
LINFEI NIE
Keyword(s):  
Sufficient Conditions ◽  
Lyapunov Functionals ◽  
Feedback Controls ◽  
Volterra Type ◽  
Competitive Systems ◽  
Analysis Technique

The paper discusses nonautonomous discrete Lotka–Volterra type n-species competitive systems with pure-delays and feedback controls. New sufficient conditions for which a part of the n-species remains permanent and others is driven to extinction are established by using the method of multiple discrete Lyapunov functionals and introducing new analysis technique. Our results show that the feedback controls cannot influence the permanence of species.

scholarly journals Dynamics in a Delayed Competition System on a Weighted Network

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yaohua Tong ◽  
Xiaoling Wang
Keyword(s):  
Steady State ◽  
Time Delays ◽  
Complex Dynamics ◽  
Sufficient Conditions ◽  
Weighted Network ◽  
Competition System ◽  
Numerical Examples ◽  
Competitive Systems ◽  
Positive Steady States ◽  
The Stability

In this paper, we study the stability of positive steady states in a delayed competition system on a weighted network, which does not satisfy the comparison principle appealing to classical competitive systems. By introducing some auxiliary equations and constructing proper contracting rectangles, we present some sufficient conditions on the stability of the unique positive steady state. Moreover, some numerical examples are given to explore the complex dynamics of this nonmonotone model, which implies the nontrivial roles of weights and time delays.

scholarly journals Lorenz System Stabilization Using Fuzzy Controllers

2007 ◽  
Vol 2 (3) ◽  
pp. 279 ◽  
Author(s):  
Radu-Emil Precup ◽  
Marius L. Tomescu ◽  
Stefan Preitl
Keyword(s):  
Stability Analysis ◽  
Chaotic Systems ◽  
Fuzzy Logic Controller ◽  
Lorenz System ◽  
Sufficient Conditions ◽  
Fuzzy Rule ◽  
Analysis Method ◽  
The Lorenz System ◽  
The Stability ◽  
Takagi Sugeno

The paper suggests a Takagi Sugeno (TS) fuzzy logic controller (FLC) designed to stabilize the Lorentz chaotic systems. The stability analysis of the fuzzy control system is performed using Barbashin-Krasovskii theorem. This paper proves that if the derivative of Lyapunov function is negative semi-definite for each fuzzy rule then the controlled Lorentz system is asymptotically stable in the sense of Lyapunov. The stability theorem suggested here offers sufficient conditions for the stability of the Lorenz system controlled by TS FLCs. An illustrative example describes the application of the new stability analysis method.

GLOBAL EXPONENTIAL STABILITY CONDITIONS FOR DELAYED PARABOLIC NEURAL NETWORKS WITH VARIABLE COEFFICIENTS

2007 ◽  
Vol 17 (12) ◽  
pp. 4409-4415
Author(s):  
XUYANG LOU ◽  
BAOTONG CUI
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Variable Coefficients ◽  
Lyapunov Functionals ◽  
The Stability ◽  
Delay Differential ◽  
Delay Differential Inequality

In this paper, we present a class of delayed parabolic neural networks (DPNN) with variable coefficients. Some sufficient conditions for the global exponential stability of the DPNN with variable coefficients are derived by a method based on delay differential inequality. The method, which does not make use of Lyapunov functionals, is simple and effective for the stability analysis of DPNN with variable coefficients.

scholarly journals Dynamic Behaviors of a General Discrete Nonautonomous System of Plankton Allelopathy with Delays

2008 ◽  
Vol 2008 ◽  
pp. 1-22 ◽  
Author(s):  
Yaoping Chen ◽  
Fengde Chen ◽  
Zhong Li
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Functional ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Nonautonomous System ◽  
Suitable Assumption ◽  
Dynamic Behaviors ◽  
Plankton Allelopathy

We study the dynamic behaviors of a general discrete nonautonomous system of plankton allelopathy with delays. We first show that under some suitable assumption, the system is permanent. Next, by constructing a suitable Lyapunov functional, we obtain a set of sufficient conditions which guarantee the global attractivity of the two species. After that, by constructing an extinction-type Lyapunov functional, we show that under some suitable assumptions, one species will be driven to extinction. Finally, two examples together with their numerical simulations show the feasibility of the main results.

Dynamical analysis of a two-species competitive system with state feedback impulsive control

2020 ◽  
Vol 13 (05) ◽  
pp. 2050007
Author(s):  
Jing Xu ◽  
Mingzhan Huang ◽  
Xinyu Song
Keyword(s):  
Periodic Solution ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Dynamical Analysis ◽  
Competitive System ◽  
Competitive Systems ◽  
State Dependent ◽  
Existence And Stability ◽  
The Stability ◽  
Theoretical Results

In this paper, three competitive systems with different kinds of state-dependent control are presented and investigated. The existence of the order-1 homoclinic orbit and order-1 periodic solution of the two systems that incorporate just one kind of state-dependent control is obtained by applying differential equation geometry theory, and the stability of the order-1 periodic solution of each system is also given. Besides, sufficient conditions for the existence and stability of the order-2 periodic solution of the system that incorporate two kinds of state-dependent control are gained by successor function method and analogue of Poincaré criterion, respectively. Finally, numerical simulations are carried out to verify the theoretical results.

Stochastic epidemic dynamics based on the association between susceptible and recovered individuals

2020 ◽  
pp. 2050085
Author(s):  
Luyao Xin ◽  
Yingxin Guo ◽  
Quanxin Zhu
Keyword(s):  
Mathematical Model ◽  
White Noise ◽  
Numerical Simulations ◽  
Sufficient Conditions ◽  
Deterministic Case ◽  
Epidemic Dynamics ◽  
Stochastic Epidemic ◽  
The Stability ◽  
Permanence In Mean ◽  
Theoretical Results

In this paper, we propose a new mathematical model based on the association between susceptible and recovered individual. Then, we study the stability of this model with the deterministic case and obtain the conditions for the extinction of diseases. Moreover, in view of the association between susceptible and recovered individual perturbed by white noise, we also give sufficient conditions for the extinction and the permanence in mean of disease with the white noise. Finally, we have numerical simulations to demonstrate the correctness of obtained theoretical results.

scholarly journals Dynamic Complexity of an Ivlev-Type Prey-Predator System with Impulsive State Feedback Control

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Chuanjun Dai ◽  
Min Zhao ◽  
Lansun Chen
Keyword(s):  
Feedback Control ◽  
Numerical Simulations ◽  
State Feedback ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Bifurcation Diagrams ◽  
Dynamic Complexity ◽  
Impulsive State Feedback Control ◽  
The Stability ◽  
Predator System

The dynamic complexities of an Ivlev-type prey-predator system with impulsive state feedback control are studied analytically and numerically. Using the analogue of the Poincaré criterion, sufficient conditions for the existence and the stability of semitrivial periodic solutions can be obtained. Furthermore, the bifurcation diagrams and phase diagrams are investigated by means of numerical simulations, which illustrate the feasibility of the main results presented here.

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