scholarly journals Extinction and Permanence of a Three-Species Lotka-Volterra System with Impulsive Control Strategies

2008 ◽  
Vol 2008 ◽  
pp. 1-18 ◽  
Author(s):  
Hunki Baek
Keyword(s):  
Chemical Control ◽  
Small Amplitude ◽  
Floquet Theory ◽  
Impulsive Control ◽  
Chaotic Behavior ◽  
Control Strategies ◽  
Perturbation Techniques ◽  
Top Predator ◽  
Volterra System ◽  
Comparison Results

A three-species Lotka-Volterra system with impulsive control strategies containing the biological control (the constant impulse) and the chemical control (the proportional impulse) with the same period, but not simultaneously, is investigated. By applying the Floquet theory of impulsive differential equation and small amplitude perturbation techniques to the system, we find conditions for local and global stabilities of a lower-level prey and top-predator free periodic solution of the system. In addition, it is shown that the system is permanent under some conditions by using comparison results of impulsive differential inequalities. We also give a numerical example that seems to indicate the existence of chaotic behavior.

scholarly journals Dynamics of a Beddington-DeAngelis Type Predator-Prey Model with Impulsive Effect

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Sun Shulin ◽  
Guo Cuihua
Keyword(s):  
Small Amplitude ◽  
Floquet Theory ◽  
Impulsive Control ◽  
Control Strategies ◽  
Impulsive Effect ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Impulsive Equation ◽  
Predator System ◽  
Comparison Technique

In view of the logical consistence, the model of a two-prey one-predator system with Beddington-DeAngelis functional response and impulsive control strategies is formulated and studied systematically. By using the Floquet theory of impulsive equation, small amplitude perturbation method, and comparison technique, we obtain the conditions which guarantee the global asymptotic stability of the two-prey eradication periodic solution. We also proved that the system is permanent under some conditions. Numerical simulations find that the system appears the phenomenon of competition exclusion.

scholarly journals Complex Behavior in a Fish Algae Consumption Model with Impulsive Control Strategy

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Jin Yang ◽  
Min Zhao
Keyword(s):  
Control Strategy ◽  
Small Amplitude ◽  
Impulsive Control ◽  
Asymptotically Stable ◽  
Perturbation Techniques ◽  
Globally Asymptotically Stable ◽  
Impulsive Equations ◽  
Consumption Model ◽  
The Rich ◽  
Impulsive Control Strategy

This paper investigates a dynamic mathematical model of fish algae consumption with an impulsive control strategy analytically. It is proved that the system has a globally asymptotically stable algae-eradication periodic solution and is permanent by using the theory of impulsive equations and small-amplitude perturbation techniques. Numerical results for impulsive perturbations demonstrate the rich dynamic behavior of the system. Further, we have also compared biological control with chemical control. All these results may be useful in controlling eutrophication.

scholarly journals Stability and Permanence of a Pest Management Model with Impulsive Releasing and Harvesting

2013 ◽  
Vol 2013 ◽  
pp. 1-18 ◽  
Author(s):  
Jiangtao Yang ◽  
Zhichun Yang
Keyword(s):  
Pest Management ◽  
Small Amplitude ◽  
Floquet Theory ◽  
Sufficient Conditions ◽  
Management Model ◽  
Perturbation Techniques ◽  
Globally Asymptotical Stability ◽  
Period Solution ◽  
Impulsive Releasing ◽  
Theoretical Results

We formulate a pest management model with periodically releasing infective pests, immature and mature natural enemies, and harvesting pests and crops at two different fixed moments. Sufficient conditions ensuring the locally and globally asymptotical stability of the susceptible pest-eradication period solution are found by means of Floquet theory, small amplitude perturbation techniques, and multicomparison results. Furthermore, the permanence of system is also derived. By numerical analysis, we also show that impulsive releasing and harvesting at two different fixed moments can bring obvious effects on the dynamics of system, which also corroborates our theoretical results.

scholarly journals A Mathematical Model for the Dynamics of a Fish Algae Consumption Model with Impulsive Control Strategy

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Jin Yang ◽  
Min Zhao
Keyword(s):  
Mathematical Model ◽  
Control Strategy ◽  
Floquet Theory ◽  
Impulsive Control ◽  
Impulsive Differential Equations ◽  
Asymptotically Stable ◽  
Perturbation Techniques ◽  
Globally Asymptotically Stable ◽  
The Rich ◽  
Impulsive Control Strategy

A dynamic mathematical model of fish algae consumption with an impulsive control strategy is proposed and analyzed in detail. It is shown that the system has a globally asymptotically stable algae-eradication periodic solution which can be obtained using the Floquet theory of impulsive differential equations and small-amplitude perturbation techniques. The conditions for the permanence of the system can also be determined. Numerical results for impulsive perturbations show the rich dynamic behavior of the system. All these results may be useful in controlling eutrophication.

scholarly journals Period-doubling bifurcation analysis and chaos control for load torque using FLC

2021 ◽  
Author(s):  
Eman Moustafa ◽  
Abdel-Azem Sobaih ◽  
Belal Abozalam ◽  
Amged Sayed A. Mahmoud
Keyword(s):  
Floquet Theory ◽  
Chaos Control ◽  
Fuzzy Logic Controller ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Parameter Variation ◽  
Period Doubling Bifurcation ◽  
Load Torque ◽  
Nonlinear Behaviors ◽  
Scientific Fields

AbstractChaotic phenomena are observed in several practical and scientific fields; however, the chaos is harmful to systems as they can lead them to be unstable. Consequently, the purpose of this study is to analyze the bifurcation of permanent magnet direct current (PMDC) motor and develop a controller that can suppress chaotic behavior resulted from parameter variation such as the loading effect. The nonlinear behaviors of PMDC motors were investigated by time-domain waveform, phase portrait, and Floquet theory. By varying the load torque, a period-doubling bifurcation appeared which in turn led to chaotic behavior in the system. So, a fuzzy logic controller and developing the Floquet theory techniques are applied to eliminate the bifurcation and the chaos effects. The controller is used to enhance the performance of the system by getting a faster response without overshoot or oscillation, moreover, tends to reduce the steady-state error while maintaining its stability. The simulation results emphasize that fuzzy control provides better performance than that obtained from the other controller.

Impulsive Control and Synchronization of Memristor-Based Chaotic Circuits

2014 ◽  
Vol 24 (12) ◽  
pp. 1450162 ◽  
Author(s):  
Shiju Yang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Chaotic System ◽  
Impulsive Control ◽  
Chaotic Behavior ◽  
Memory Function ◽  
Sufficient Conditions ◽  
Impulsive System ◽  
Circuit Element ◽  
Chaotic Circuits ◽  
Control And Synchronization ◽  
Passive Circuit

The memristor is a novel nonlinear passive circuit element which has the memory function, and the circuits based on the memristors might exhibit chaotic behavior. In this paper, we revisit a memristor-based chaotic circuit, and then investigate its stabilization and synchronization via impulsive control. By impulsive system theory, some sufficient conditions for the stabilization and synchronization of the memristor-based chaotic system are established. Moreover, an estimation of the upper bound of the impulse interval is proposed under the condition that the parameters of the chaotic system and the impulsive control law are well defined. To show the effectiveness of the theoretical results, numerical simulations are also presented.

Determination of Instability Boundaries for a Highly Flexible Prismatic-Jointed Robot Performing Repetitive Maneuvers

1991 ◽  
Author(s):  
Keith W. Buffinton
Keyword(s):  
Floquet Theory ◽  
Equations Of Motion ◽  
Perturbation Techniques ◽  
Axial Motion ◽  
The Third ◽  
Straightforward Application ◽  
Method Yield ◽  
Robotic Devices ◽  
Axially Moving

Abstract Presented in this work are the equations of motion governing the behavior of a simple, highly flexible, prismatic-jointed robotic manipulator performing repetitive maneuvers. The robot is modeled as a uniform cantilever beam that is subject to harmonic axial motions over a single bilateral support. To conveniently and accurately predict motions that lead to unstable behavior, three methods are investigated for determining the boundaries of unstable regions in the parameter space defined by the amplitude and frequency of axial motion. The first method is based on a straightforward application of Floquet theory; the second makes use of the results of a perturbation analysis; and the third employs Bolotin’s infinite determinate method. Results indicate that both perturbation techniques and Bolotin’s method yield acceptably accurate results for only very small amplitudes of axial motion and that a direct application of Floquet theory, while computational expensive, is the most reliable way to ensure that all instability boundaries are correctly represented. These results are particularly relevant to the study of prismatic-jointed robotic devices that experience amplitudes of periodic motion that are a significant percentage of the length of the axially moving member.

Chaos Control for a Fractional-Order Jerk System via Time Delay Feedback Controller and Mixed Controller

2021 ◽  
Vol 5 (4) ◽  
pp. 257
Author(s):  
Changjin Xu ◽  
Maoxin Liao ◽  
Peiluan Li ◽  
Lingyun Yao ◽  
Qiwen Qin ◽  
...  
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Chaos Control ◽  
Chaotic Behavior ◽  
Control Strategies ◽  
Feedback Controller ◽  
Research Approach ◽  
Controlling Chaos ◽  
The Stability ◽  
Jerk System

In this study, we propose a novel fractional-order Jerk system. Experiments show that, under some suitable parameters, the fractional-order Jerk system displays a chaotic phenomenon. In order to suppress the chaotic behavior of the fractional-order Jerk system, we design two control strategies. Firstly, we design an appropriate time delay feedback controller to suppress the chaos of the fractional-order Jerk system. The delay-independent stability and bifurcation conditions are established. Secondly, we design a suitable mixed controller, which includes a time delay feedback controller and a fractional-order PDσ controller, to eliminate the chaos of the fractional-order Jerk system. The sufficient condition ensuring the stability and the creation of Hopf bifurcation for the fractional-order controlled Jerk system is derived. Finally, computer simulations are executed to verify the feasibility of the designed controllers. The derived results of this study are absolutely new and possess potential application value in controlling chaos in physics. Moreover, the research approach also enriches the chaos control theory of fractional-order dynamical system.

scholarly journals An Impulsively Controlled Three-Species Prey-Predator Model with Stage Structure and Birth Pulse for Predator

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Yanyan Hu ◽  
Mei Yan ◽  
Zhongyi Xiang
Keyword(s):  
Small Amplitude ◽  
Floquet Theory ◽  
Stage Structure ◽  
Critical Value ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Birth Pulse ◽  
Impulsive Equation ◽  
Predator Model ◽  
Predator System

We investigate the dynamic behaviors of a two-prey one-predator system with stage structure and birth pulse for predator. By using the Floquet theory of linear periodic impulsive equation and small amplitude perturbation method, we show that there exists a globally asymptotically stable two-prey eradication periodic solution when the impulsive period is less than some critical value. Further, we study the permanence of the investigated model. Our results provide valuable strategy for biological economics management. Numerical analysis is also inserted to illustrate the results.

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