Complex Dynamical Behavior of a Three Species Prey–Predator System with Nonlinear Harvesting

2020 ◽  
Vol 30 (13) ◽  
pp. 2050195
Author(s):  
R. P. Gupta ◽  
Dinesh K. Yadav
Keyword(s):  
Dynamical Behavior ◽  
Local Existence ◽  
Steady States ◽  
Trophic Levels ◽  
System A ◽  
Persistence Conditions ◽  
Proposed Model ◽  
Positive Steady States ◽  
Nonlinear Harvesting ◽  
Predator System

In this manuscript, we consider an extended version of the prey–predator system with nonlinear harvesting [Gupta et al., 2015] by introducing a top predator (omnivore) which feeds on more than one trophic levels. Consideration of third species as omnivore makes the system a food web of three populations. We have guaranteed positivity as well as the boundedness of solutions of the proposed system. We observed that the presence of third species complicates the dynamical behavior of the system. It is also observed that multiple positive steady states exist for the proposed system which makes the problem more interesting compared to the similar models studied previously. Sotomayor’s theorem is being utilized to study the saddle-node bifurcation. The persistence conditions are discussed for the proposed model. The local existence of periodic solution through Hopf bifurcations is also guaranteed numerically. It is observed that the proposed model is capable to exhibit more complicated dynamics in the form of chaos in both the cases when there are unique and multiple coexisting steady states. Bifurcation diagrams and Lyapunov exponents have been drawn to ensure the existence of chaotic dynamics of the system.

DYNAMICAL BEHAVIOR IN A HARVESTED DIFFERENTIAL-ALGEBRAIC PREY-PREDATOR MODEL

2009 ◽  
Vol 02 (04) ◽  
pp. 463-482 ◽  
Author(s):  
CHAO LIU ◽  
QINGLING ZHANG ◽  
XUE ZHANG ◽  
XIAODONG DUAN
Keyword(s):  
Bifurcation Theory ◽  
State Feedback ◽  
Dynamical Behavior ◽  
Algebraic Model ◽  
Economic Interest ◽  
Interior Equilibrium ◽  
Proposed Model ◽  
Differential Algebraic System ◽  
Predator Model ◽  
Predator System

A differential-algebraic model which considers a prey-predator system with harvest effort on predator is proposed. By using the differential-algebraic system theory and bifurcation theory, local stability of the proposed model around the interior equilibrium is investigated. Furthermore, the instability mechanism of the proposed model due to the variation of economic interest of harvesting is studied. With the purpose of stabilizing the proposed model around the interior equilibrium and maintaining the economic interest of harvesting at an ideal level, a state feedback controller is designed. Finally, numerical simulations are carried out to show the consistency with theoretical analysis.

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 Order and Chaos in a Prey-Predator Model Incorporating Refuge, Disease, and Harvesting

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Dahlia Khaled Bahlool ◽  
Huda Abdul Satar ◽  
Hiba Abdullah Ibrahim
Keyword(s):  
Equilibrium Points ◽  
Global Dynamics ◽  
Persistence Conditions ◽  
Local Bifurcation Analysis ◽  
Uniqueness Of The Solution ◽  
Harvesting Process ◽  
Predator Model ◽  
The Stability ◽  
Predator System ◽  
Type Ii Functional Response

In this paper, a mathematical model consisting of a prey-predator system incorporating infectious disease in the prey has been proposed and analyzed. It is assumed that the predator preys upon the nonrefugees prey only according to the modified Holling type-II functional response. There is a harvesting process from the predator. The existence and uniqueness of the solution in addition to their bounded are discussed. The stability analysis of the model around all possible equilibrium points is investigated. The persistence conditions of the system are established. Local bifurcation analysis in view of the Sotomayor theorem is carried out. Numerical simulation has been applied to investigate the global dynamics and specify the effect of varying the parameters. It is observed that the system has a chaotic dynamics.

Switching effect on the stability of the prey-predator system with three trophic levels

1986 ◽  
Vol 122 (3) ◽  
pp. 251-262 ◽  
Author(s):  
Hiroyuki Matsuda ◽  
Kohkichi Kawasaki ◽  
Nanako Shigesada ◽  
Ei Teramoto ◽  
Luigi M. Ricciardi
Keyword(s):  
Trophic Levels ◽  
Switching Effect ◽  
The Stability ◽  
Predator System

scholarly journals Zero Eigenvalue Analysis for the Determination of Multiple Steady States in Reaction Networks

1998 ◽  
Vol 53 (3-4) ◽  
pp. 171-177
Author(s):  
Hsing-Ya Li
Keyword(s):  
Steady State ◽  
Rate Constants ◽  
Reaction Network ◽  
Steady States ◽  
Eigenvalue Analysis ◽  
Zero Eigenvalue ◽  
Positive Steady State ◽  
Positive Steady States ◽  
Positive Rate ◽  
System Of Inequalities

Abstract A chemical reaction network can admit multiple positive steady states if and only if there exists a positive steady state having a zero eigenvalue with its eigenvector in the stoichiometric subspace. A zero eigenvalue analysis is proposed which provides a necessary and sufficient condition to determine the possibility of the existence of such a steady state. The condition forms a system of inequalities and equations. If a set of solutions for the system is found, then the network under study is able to admit multiple positive steady states for some positive rate constants. Otherwise, the network can exhibit at most one steady state, no matter what positive rate constants the system might have. The construction of a zero-eigenvalue positive steady state and a set of positive rate constants is also presented. The analysis is demonstrated by two examples.

scholarly journals Modeling and Implementation of MPPT based Wind Energy System Using Cuckoo Search

2018 ◽  
Vol 7 (2.7) ◽  
pp. 671
Author(s):  
Kaleem SK ◽  
Rama Subbanna S
Keyword(s):  
Wind Energy ◽  
Control Strategy ◽  
Cuckoo Search ◽  
Energy System ◽  
System A ◽  
Wind Turbine System ◽  
Proposed Model ◽  
Wind Energy System ◽  
Mppt Controller ◽  
And Performance

This paper presents adjustable speed generators for wind turbines. In order to improve the potential and performance of wind turbine system this paper proposes a concept DFIG. Generally wind nature is not fixed it varies linearly w.r.t time, hence, a MPPT controller is proposed in this paper. This paper presents the DFIG wind energy system. A Control strategy implemented and controlled by framing rotor reference frame axis in terms of direct and quadrature axis coordinates. A PI based RSC and GSC controllers are introduced to control the power through the wind system to grid. This proposed model is implemented and verified by using Matlab/Simulink.  

scholarly journals Development of integrated multi-trophic aquaculture (IMTA) for tropical brackishwater species in Sindhudurg District, Maharashtra, west coast of India

2018 ◽  
Vol 65 (1) ◽  
Author(s):  
C. P. Balasubramanian ◽  
Shailesh S. Mhaskar ◽  
Krishna Sukumaran ◽  
A. Panigrahi ◽  
Kurmaraguru Vasagam ◽  
...  
Keyword(s):  
Experimental System ◽  
Open Water ◽  
Trophic Levels ◽  
Cost Ratio ◽  
Benefit Cost Ratio ◽  
System A ◽  
Etroplus Suratensis ◽  
Penaeus Indicus ◽  
Benefit Cost ◽  
And Control

Integrated multi-trophic aquaculture (IMTA), farming of species from different trophic levels and with complimentary ecosystem function, is regarded as a suitable approach to develop a sustainable aquaculture system. In order to establish an IMTA system, a study was carried out in Sindhudurg District, Maharashtra, India for selected tropical brackish-water species. Two equal sized pens (250 m2) were constructed for IMTA and control respectively in each land based system and open water cages were set in the estuary. Different combinations of fed species (Chanos chanos, Etroplus suratensis, Mugil cephalus, Penaeus indicus) and an extractive crop (Crassostrea madrasensis) were stocked in IMTA experimental system whereas monoculture of P. indicus served as control. Water quality characteristics were found to be within the admissible limits. Soil organic carbon was found to be lesser in the IMTA system compared to control. The productivity of IMTA system was higher than control: 3250 kg h-1 vs 2000 kg ha-1. Further, income and benefit-cost ratio was found to be higher in IMTA pens. The present study concludes that IMTA is a possible option for system diversification as well as species diversification without compromising economic profitability of culture.

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