scholarly journals The Modelling and Control of a Singular Biological Economic System in a Polluted Environment

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Yi Zhang ◽  
Yueming Jie ◽  
Xinyou Meng
Keyword(s):  
Bifurcation Theory ◽  
State Feedback ◽  
Singular Systems ◽  
Stage Structure ◽  
Fishing Effort ◽  
Positive Equilibrium ◽  
Economic Profit ◽  
Singularity Induced Bifurcation ◽  
And Control ◽  
Theoretical Results

A singular biological economic model with harvesting and stage structure is presented. The local stability of equilibriums of the system is investigated when the economic profit parameter is zero, and the conditions of the singularity induced bifurcation occurring at the positive equilibrium are obtained by the singular systems theory and bifurcation theory. In order to eliminate the singularity induced bifurcation, a state feedback controller is designed by controlling the fishing effort. At last, an application example is given to illustrate the validity of the theoretical results.

scholarly journals Bifurcation and Feedback Control of an Exploited Prey-Predator System

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Uttam Das
Keyword(s):  
Theoretical Analysis ◽  
State Feedback ◽  
Dynamical Behavior ◽  
Algebraic Model ◽  
Positive Equilibrium ◽  
Economic Interest ◽  
Economic Profit ◽  
Proposed Model ◽  
Singularity Induced Bifurcation ◽  
Predator System

This paper makes an attempt to highlight a differential algebraic model in order to investigate the dynamical behavior of a prey-predator system due to the variation of economic interest of harvesting. In this regard, it is observed that the model exhibits a singularity induced bifurcation when economic profit is zero. For the purpose of stabilizing the proposed model at the positive equilibrium, a state feedback controller is therefore designed. Finally, some numerical simulations are carried out to show the consistency with theoretical analysis and to illustrate the effectiveness of the proposed controller.

scholarly journals StochasticH∞Control for Discrete-Time Singular Systems with State and Disturbance Dependent Noise

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Yong Zhao ◽  
Xiushan Jiang ◽  
Weihai Zhang
Keyword(s):  
Discrete Time ◽  
State Feedback ◽  
Closed Loop ◽  
Singular Systems ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Mean Square ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Theoretical Results

This paper is concerned with the stochasticH∞state feedback control problem for a class of discrete-time singular systems with state and disturbance dependent noise. Two stochastic bounded real lemmas (SBRLs) are proposed via strict linear matrix inequalities (LMIs). Based on the obtained SBRLs, a state feedbackH∞controller is presented, which not only guarantees the resulting closed-loop system to be mean square admissible but also satisfies a prescribedH∞performance level. A numerical example is finally given to illustrate the effectiveness of the proposed theoretical results.

scholarly journals Complex Dynamics in a Singular Delayed Bioeconomic Model with and without Stochastic Fluctuation

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Xinyou Meng ◽  
Qingling Zhang
Keyword(s):  
Hopf Bifurcation ◽  
Complex Dynamics ◽  
Hybrid Control ◽  
Positive Equilibrium ◽  
Stochastic Fluctuation ◽  
Predator Prey ◽  
Prey System ◽  
Singularity Induced Bifurcation ◽  
Distribution Of Roots ◽  
Theoretical Results

A singular delayed biological economic predator-prey system with and without stochastic fluctuation is proposed. The conditions of singularity induced bifurcation are gained, and a state feedback controller is designed to eliminate such bifurcation. Furthermore, saddle-node bifurcation is also showed. Next, the local stability of the positive equilibrium and the existence of Hopf bifurcation are obtained by analyzing the distribution of roots of the corresponding characteristic equation, and the hybrid control strategy is used to control the occurrence of Hopf bifurcation. In addition, some explicit formulas determining the spectral densities of the populations and harvest effort are given when the system is considered with stochastic fluctuation. Finally, numerical simulations are illustrated to verify the theoretical results.

scholarly journals Codimension-2 Bifurcation Analysis and Control of a Discrete Mosquito Model with a Proportional Release Rate of Sterile Mosquitoes

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Qiaoling Chen ◽  
Zhidong Teng ◽  
Junli Liu ◽  
Feng Wang
Keyword(s):  
Release Rate ◽  
Discrete Model ◽  
Bifurcation Theory ◽  
Control Strategies ◽  
Phase Portraits ◽  
Bifurcation Diagrams ◽  
Dynamical Behaviors ◽  
And Control ◽  
Theoretical Results ◽  
Maximum Lyapunov Exponents

This paper concerns a discrete wild and sterile mosquito model with a proportional release rate of sterile mosquitoes. It is shown that the discrete model undergoes codimension-2 bifurcations with 1 : 2, 1 : 3, and 1 : 4 strong resonances by applying the bifurcation theory. Some numerical simulations, including codimension-2 bifurcation diagrams, maximum Lyapunov exponents diagrams, and phase portraits, are also presented to illustrate the validity of theoretical results and display the complex dynamical behaviors. Moreover, two control strategies are applied to the model.

BIFURCATION AND CONTROL IN A DIFFERENTIAL-ALGEBRAIC HARVESTED PREY-PREDATOR MODEL WITH STAGE STRUCTURE FOR PREDATOR

2008 ◽  
Vol 18 (10) ◽  
pp. 3159-3168 ◽  
Author(s):  
CHAO LIU ◽  
QINGLING ZHANG ◽  
YUE ZHANG ◽  
XIAODONG DUAN
Keyword(s):  
Stage Structure ◽  
Algebraic Model ◽  
Model System ◽  
Positive Equilibrium ◽  
Proposed Model ◽  
Stability And Instability ◽  
Differential Algebraic System ◽  
Predator Model ◽  
And Control ◽  
Predator System

A differential-algebraic model system which considers a prey-predator system with stage structure for a predator and a harvest effort on the mature predator is proposed. By using the differential-algebraic system and bifurcation theories, the local stability and instability mechanism of the proposed model system are investigated. With the purpose of stabilizing the proposed model system at the positive equilibrium, a state feedback controller is designed. Finally, a numerical simulation is carried out to show the consistency with theoretical analysis and illustrate the effectiveness of the proposed controller.

scholarly journals Global Stability for a Delayed Predator-Prey System with Stage Structure for the Predator

2009 ◽  
Vol 2009 ◽  
pp. 1-24
Author(s):  
Xiao Zhang ◽  
Rui Xu ◽  
Qintao Gan
Keyword(s):  
Global Stability ◽  
Local Stability ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Positive Equilibrium ◽  
Predator Prey ◽  
Prey System ◽  
Comparison Argument ◽  
Theoretical Results ◽  
Iteration Technique

A delayed predator-prey system with stage structure for the predator is investigated. By analyzing the corresponding characteristic equations, the local stability of equilibria of the system is discussed. The existence of Hopf bifurcation at the positive equilibrium is established. By using an iteration technique and comparison argument, respectively, sufficient conditions are derived for the global stability of the positive equilibrium and two boundary equilibria of the system. Numerical simulations are carried out to illustrate the theoretical results.

scholarly journals Stability and Bifurcation Analysis of a Nonlinear Discrete Logistic Model with Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Daiyong Wu ◽  
Hai Zhang ◽  
Jinde Cao ◽  
Tasawar Hayat
Keyword(s):  
Asymptotic Stability ◽  
Logistic Model ◽  
Bifurcation Theory ◽  
Polynomial Equation ◽  
Positive Equilibrium ◽  
Stability And Bifurcation Analysis ◽  
Linearized System ◽  
Bifurcation Direction ◽  
The Stability ◽  
Theoretical Results

We consider a nonlinear discrete logistic model with delay. The characteristic equation of the linearized system at the positive equilibrium is a polynomial equation involving high order terms. We obtain the conditions ensuring the asymptotic stability of the positive equilibrium and the existence of Neimark-Sacker bifurcation, with respect to the parameter of the model. Based on the bifurcation theory, we discuss Neimark-Sacker bifurcation direction and the stability of bifurcated solutions. Finally, some numerical simulations are performed to illustrate the theoretical results.

Global dissipativity and exponential synchronization of mixed time-varying delays neural networks with discontinuous activations

2020 ◽  
Vol 21 (7-8) ◽  
pp. 693-704 ◽  
Author(s):  
Kaifang Fei ◽  
Minghui Jiang ◽  
Meng Yan ◽  
Weizhen Liu
Keyword(s):  
Neural Networks ◽  
State Feedback ◽  
Exponential Synchronization ◽  
Matrix Measure ◽  
Analysis Techniques ◽  
Discontinuous Activations ◽  
Inclusion Theory ◽  
Generalized Halanay Inequality ◽  
New Criteria ◽  
Theoretical Results

AbstractIn this paper, the matters of dissipativity and synchronization for non-autonomous Hopfield neural networks with discontinuous activations are investigated. Firstly, under the framework of extending Filippov differential inclusion theory, several effective new criteria are derived. The global dissipativity of Filippov solution to neural networks is proved by using generalized Halanay inequality and matrix measure method. Secondly, the global exponential synchronization of the addressed network drive system and the response system is realized by utilizing inequality and some analysis techniques and designing the discontinuous state feedback controller. Finally, several numerical examples are given to verify the validity of the theoretical results.

A prey–predator model and control of a nematodes pest using control in banana: Mathematical modeling and qualitative analysis

2021 ◽  
pp. 2150089
Author(s):  
Sudhakar Yadav ◽  
Vivek Kumar
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Local Stability ◽  
Detection Method ◽  
Initial Release ◽  
Pest Detection ◽  
Predator Model ◽  
And Control ◽  
The Mathematical Model ◽  
Theoretical Results

This study develops a mathematical model for describing the dynamics of the banana-nematodes and its pest detection method to help banana farmers. Two criteria: the mathematical model and the type of nematodes pest control system are discussed. The sensitivity analysis, local stability, global stability, and the dynamic behavior of the mathematical model are performed. Further, we also develop and discuss the optimal control mathematical model. This mathematical model represents various modes of management, including the initial release of infected predators as well as the destroying of nematodes. The theoretical results are shown and verified by numerical simulations.

Robust PD State Feedback Controller Design for Uncertain Singular Systems

2011 ◽  
Vol 403-408 ◽  
pp. 3813-3818
Author(s):  
Jian Wu Zhu ◽  
Yuan Chun Ding
Keyword(s):  
State Feedback ◽  
Controller Design ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Feedback Controller ◽  
State Feedback Controller ◽  
Closed Loop Systems ◽  
Uncertain Singular Systems ◽  
Parameter Dependent ◽  
Robust Stability And Stabilization

This paper is concerned with the problem of robust stability and stabilization of singular systems with uncertainties in both the derivative and state matrices. By using a parameter dependent Lyapunov function, we derive the LMI-based sufficient conditions for the stabilization of the singular systems. Secondly, by solving these LMIs, a proportional plus derivative (PD) state feedback controller is designed for the closed-loop systems to be quadratically normal and quadratically stable (QNQS). Finally, the numerical example is given to show the effectiveness of the proposed theorems.

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