scholarly journals Bifurcation and Chaos of a Discrete Predator-Prey Model with Crowley–Martin Functional Response Incorporating Proportional Prey Refuge

2020 ◽  
Vol 2020 ◽  
pp. 1-18 ◽  
Author(s):  
P. K. Santra ◽  
G. S. Mahapatra ◽  
G. R. Phaijoo
Keyword(s):  
Functional Response ◽  
Control Method ◽  
Equilibrium Points ◽  
Period Doubling ◽  
Phase Portraits ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Feedback Control Method ◽  
And Control

The paper investigates the dynamical behaviors of a two-species discrete predator-prey system with Crowley–Martin functional response incorporating prey refuge proportional to prey density. The existence of equilibrium points, stability of three fixed points, period-doubling bifurcation, Neimark–Sacker bifurcation, Marottos chaos, and Control Chaos are analyzed for the discrete-time domain. The time graphs, phase portraits, and bifurcation diagrams are obtained for different parameters of the model. Numerical simulations and graphics show that the discrete model exhibits rich dynamics, which also present that the system is a chaotic and complex one. This paper attempts to present a feedback control method which can stabilize chaotic orbits at an unstable equilibrium point.

scholarly journals Bifurcation Analysis and Control of a Differential-Algebraic Predator-Prey Model with Allee Effect and Time Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Xue Zhang ◽  
Qing-ling Zhang
Keyword(s):  
Time Delay ◽  
Allee Effect ◽  
Control Method ◽  
Handling Time ◽  
Delayed Feedback Control ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Feedback Control Method ◽  
Predator Model ◽  
And Control

This paper studies systematically a differential-algebraic prey-predator model with time delay and Allee effect. It shows that transcritical bifurcation appears when a variation of predator handling time is taken into account. This model also exhibits singular induced bifurcation as the economic revenue increases through zero, which causes impulsive phenomenon. It can be noted that the impulsive phenomenon can be much weaker by strengthening Allee effect in numerical simulation. On the other hand, at a critical value of time delay, the model undergoes a Hopf bifurcation; that is, the increase of time delay destabilizes the model and bifurcates into small amplitude periodic solution. Moreover, a state delayed feedback control method, which can be implemented by adjusting the harvesting effort for biological populations, is proposed to drive the differential-algebraic system to a steady state. Finally, by using Matlab software, numerical simulations illustrate the effectiveness of the results.

scholarly journals Chaotic Dynamics and Control of Discrete Ratio-Dependent Predator-Prey System

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Sarker Md. Sohel Rana
Keyword(s):  
Chaotic Dynamics ◽  
Control Method ◽  
State Feedback Control ◽  
Phase Portraits ◽  
Predator Prey ◽  
Prey System ◽  
Dynamics And Control ◽  
Feedback Control Method ◽  
Ratio Dependent ◽  
And Control

This study examines the complexity of a discrete-time predator-prey system with ratio-dependent functional response. We establish algebraically the conditions for existence of fixed points and their stability. We show that under some parametric conditions the system passes through a bifurcation (flip or Neimark-Sacker). Numerical simulations are presented not only to justify theoretical results but also to exhibit new complex behaviors which include phase portraits, orbits of periods 9, 19, and 26, invariant closed circle, and attracting chaotic sets. Moreover, we measure numerically the Lyapunov exponents and fractal dimension to confirm the chaotic dynamics of the system. Finally, a state feedback control method is applied to control chaos which exists in the system.

Bifurcation analysis and control of a delayed stage-structured predator–prey model with ratio-dependent Holling type III functional response

2019 ◽  
Vol 26 (13-14) ◽  
pp. 1232-1245
Author(s):  
Miao Peng ◽  
Zhengdi Zhang
Keyword(s):  
Hopf Bifurcation ◽  
Functional Response ◽  
Control Method ◽  
Equilibrium Points ◽  
Predator Prey ◽  
Center Manifold Theorem ◽  
Type Iii ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent

A delayed stage-structured predator–prey model with ratio-dependent Holling type III functional response is proposed and explored in this study. We discuss the positivity and the existence of equilibrium points. By choosing time delay as the bifurcation parameter and analyzing the relevant characteristic equations, the local stability of the trivial equilibrium, the predator-extinction equilibrium, and the coexistence equilibrium of the system is investigated. In accordance with the normal form method and center manifold theorem, the property analysis of Hopf bifurcation of the system is obtained. Furthermore, for the purpose of protecting the stability of such a biological system, a hybrid control method is presented to control the Hopf bifurcation. Finally, numerical examples are given to verify the theoretical findings.

scholarly journals Dynamical Analysis Predator-Prey Population with Holling Type II Functional Response

2021 ◽  
Author(s):  
FE. Universitas Andi Djemma
Keyword(s):  
Functional Response ◽  
Equilibrium Points ◽  
Dynamical Analysis ◽  
Type Ii ◽  
Asymptotically Stable ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Type Ii Functional Response

In this article, we investigate the dynamical analysis of predator prey model. Interactionamong preys and predators use Holling type II functional response, and assuming prey refuge aswell as harvesting in both populations. This study aims to study the predator prey model and todetermine the effect of overharvesting which consequently will affect the ecosystem. In the modelfound three equilibrium points, i.e., (0,0) is the extinction of predator and prey equilibrium,?(??, 0) is the equilibrium with predatory populations extinct and the last equilibrium points?(??, ??) is the coexist equilibrium. All equilibrium points are asymptotically stable (locally) undercertain conditions. These analytical findings were confirmed by several numerical simulations.

scholarly journals Autonomous Jerk Oscillator with Cosine Hyperbolic Nonlinearity: Analysis, FPGA Implementation, and Synchronization

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Sifeu Takougang Kingni ◽  
Gaetan Fautso Kuiate ◽  
Victor Kamdoum Tamba ◽  
Viet-Thanh Pham
Keyword(s):  
Control Method ◽  
Sliding Mode ◽  
Equilibrium Points ◽  
Period Doubling ◽  
Fpga Implementation ◽  
Phase Portraits ◽  
Adaptive Sliding Mode Control ◽  
Coexistence Of Attractors ◽  
Route To Chaos ◽  
Two Parameters

A two-parameter autonomous jerk oscillator with a cosine hyperbolic nonlinearity is proposed in this paper. Firstly, the stability of equilibrium points of proposed autonomous jerk oscillator is investigated by analyzing the characteristic equation and the existence of Hopf bifurcation is verified using one of the two parameters as a bifurcation parameter. By tuning its two parameters, various dynamical behaviors are found in the proposed autonomous jerk oscillator including periodic attractor, one-scroll chaotic attractor, and coexistence between chaotic and periodic attractors. The proposed autonomous jerk oscillator has period-doubling route to chaos with the variation of one of its parameters and reverse period-doubling route to chaos with the variation of its other parameter. The proposed autonomous jerk oscillator is modelled on Field Programmable Gate Array (FPGA) and the FPGA chip statistics and phase portraits are derived. The chaotic and coexistence of attractors generated in the proposed autonomous jerk oscillator are confirmed by FPGA implementation of the proposed autonomous jerk oscillator. A good qualitative agreement is illustrated between the numerical and FPGA results. Finally synchronization of unidirectional coupled identical proposed autonomous jerk oscillators is achieved using adaptive sliding mode control method.

scholarly journals Adaptive Control of Chaos in Chua's Circuit

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Weiping Guo ◽  
Diantong Liu
Keyword(s):  
Feedback Control ◽  
Control Method ◽  
Equilibrium Points ◽  
Lyapunov Theory ◽  
Chua’S Circuit ◽  
Control Of Chaos ◽  
Chua's Circuit ◽  
Adaptive Technology ◽  
Feedback Control Method ◽  
And Control

A feedback control method and an adaptive feedback control method are proposed for Chua's circuit chaos system, which is a simple 3D autonomous system. The asymptotical stability is proven with Lyapunov theory for both of the proposed methods, and the system can be dragged to one of its three unstable equilibrium points respectively. Simulation results show that the proposed methods are valid, and control performance is improved through introducing adaptive technology.

COMPLEXITY OF AN IVLEV'S PREDATOR-PREY MODEL WITH PULSE

2007 ◽  
Vol 10 (02) ◽  
pp. 217-231 ◽  
Author(s):  
GUOPING PANG ◽  
LANSUN CHEN
Keyword(s):  
Numerical Simulations ◽  
Functional Response ◽  
Period Doubling ◽  
Impulsive System ◽  
Bifurcation Diagrams ◽  
Bifurcation And Chaos ◽  
Dynamic Complexity ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Predator System

In this paper, we investigate the extinction, permanence and dynamic complexity of the two-prey, one-predator system with Ivlev's functional response and impulsive perturbation on the predator at fixed moments. Conditions for the extinction and permanence of the system are established via the comparison theorem. Numerical simulations are carried out to explain the conclusions we obtain. Furthermore, the resulting bifurcation diagrams clearly show that the impulsive system takes on many forms of complexity including period-doubling bifurcation, period-halving bifurcation, and chaos.

Bifurcations in a Seasonally Forced Predator–Prey Model with Generalized Holling Type IV Functional Response

2016 ◽  
Vol 26 (12) ◽  
pp. 1650203 ◽  
Author(s):  
Jingli Ren ◽  
Xueping Li
Keyword(s):  
Periodic Solutions ◽  
Functional Response ◽  
Complex Dynamics ◽  
Phase Portraits ◽  
Bifurcation Diagrams ◽  
Chaotic Motions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Type Iv ◽  
Numerical Bifurcation

A seasonally forced predator–prey system with generalized Holling type IV functional response is considered in this paper. The influence of seasonal forcing on the system is investigated via numerical bifurcation analysis. Bifurcation diagrams for periodic solutions of periods one and two, containing bifurcation curves of codimension one and bifurcation points of codimension two, are obtained by means of a continuation technique, corresponding to different bifurcation cases of the unforced system illustrated in five bifurcation diagrams. The seasonally forced model exhibits more complex dynamics than the unforced one, such as stable and unstable periodic solutions of various periods, stable and unstable quasiperiodic solutions, and chaotic motions through torus destruction or cascade of period doublings. Finally, some phase portraits and corresponding Poincaré map portraits are given to illustrate these different types of solutions.

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