Complex Dynamics Due to Multiple Limit Cycle Bifurcations in a Tritrophic Food Chain Model

2019 ◽  
Vol 29 (14) ◽  
pp. 1950193
Author(s):  
Xiangyu Wang ◽  
Pei Yu
Keyword(s):  
Food Chain ◽  
Limit Cycles ◽  
Complex Dynamics ◽  
Chain Model ◽  
Stable Limit ◽  
Normal Form Theory ◽  
Bistable Phenomenon ◽  
Multiple Limit Cycle ◽  
The Stability ◽  
Food Chain Model

In this paper, we consider a tritrophic food chain model with Holling functional response types III and IV for the predator and superpredator, respectively. The main attention is focused on the stability and bifurcation of equilibria when the prey has a linear growth. Coexistence of different species is shown in the food chain, demonstrating bistable phenomenon. Hopf bifurcation is studied to show complex dynamics due to multiple limit cycles bifurcation. In particular, normal form theory is applied to prove that three limit cycles can bifurcate from an equilibrium in the vicinity of a Hopf critical point, yielding a new bistable phenomenon which involves two stable limit cycles.

RICH DYNAMICS OF A TIME-DELAYED FOOD CHAIN MODEL

2006 ◽  
Vol 14 (03) ◽  
pp. 387-412 ◽  
Author(s):  
ALAKES MAITI ◽  
G. P. SAMANTA
Keyword(s):  
Computer Simulation ◽  
Time Delay ◽  
Functional Response ◽  
Food Chain ◽  
Complex Dynamics ◽  
Chain Model ◽  
Dynamical Behaviors ◽  
Discrete Time Delay ◽  
Food Chain Model ◽  
Practical Implications

Complex dynamics of a tritrophic food chain model is discussed in this paper. The model is composed of a logistic prey, a classical Lotka-Volterra functional response for prey-predator and a ratio-dependent functional response for predator-superpredator. Dynamical behaviors such as boundedness, stability and bifurcation of the model are studied critically. The effect of discrete time-delay on the model is investigated. Computer simulation of various solutions is presented to illustrate our mathematical findings. How these ideas illuminate some of the observed properties of real populations in the field is discussed and practical implications are explored.

scholarly journals SIS MODEL WITH HARVESTING IN FOOD CHAIN MODEL

2020 ◽  
Vol 25 (1) ◽  
pp. 108
Author(s):  
Sufyan A. Wuhaib ◽  
Bilal A. Yaseen
Keyword(s):  
Mathematical Model ◽  
Food Chain ◽  
Molecular System ◽  
Chain Model ◽  
Sis Model ◽  
Periodic Boundaries ◽  
The Stability ◽  
Food Chain Model ◽  
The Mathematical Model

The aim of this study the mathematical model of the type SIS, healthy prey is infected by disease and the study proved that solution and restrictive in which the molecular system do not have periodic boundaries, then it discussed the stability of those points. the study also showed how to control the disease using the harvest so as not to become an epidemic.   http://dx.doi.org/10.25130/tjps.25.2020.017

Stability and Hopf Bifurcation of a Fractional-Order Food Chain Model With Disease and Two Delays

2020 ◽  
Vol 15 (3) ◽  
Author(s):  
Xinhe Wang ◽  
Zhen Wang ◽  
Xiao Shen
Keyword(s):  
Fractional Order ◽  
Food Chain ◽  
Positive Equilibrium ◽  
Chain Model ◽  
Two Delays ◽  
Existence Conditions ◽  
Positive Equilibrium Point ◽  
The Stability ◽  
Food Chain Model ◽  
Bifurcation And Stability

Abstract In this study, a fractional-order food chain model with disease and two delays is proposed. The existence conditions for a positive equilibrium point are given, and the stability conditions without the effects of delays are established. The effects of a single time delay and two time delays are discussed, the bifurcation and stability criteria are obtained, and the bifurcation points are calculated. To support the theoretical analysis, numerical simulations are presented.

scholarly journals SIS MODEL WITH HARVESTING IN FOOD CHAIN MODEL

2020 ◽  
Vol 25 (2) ◽  
pp. 93
Author(s):  
, Bilal A. Yaseen
Keyword(s):  
Mathematical Model ◽  
Food Chain ◽  
Molecular System ◽  
Chain Model ◽  
Sis Model ◽  
Periodic Boundaries ◽  
The Stability ◽  
Food Chain Model ◽  
The Mathematical Model

The aim of this study the mathematical model of the type SIS , healthy prey is infected by disease and the study proved that solution and restrictive in which the molecular system do not have periodic boundaries , then it discussed the stability of those points. the study also showed how to control the disease using the harvest so as not to become an epidemic   http://dx.doi.org/10.25130/tjps.25.2020.035

scholarly journals Complex dynamics of a three species food-chain model with Holling type IV functional response

2011 ◽  
Vol 16 (3) ◽  
pp. 553-374
Author(s):  
Ranjit Kumar Upadhyay ◽  
Sharada Nandan Raw
Keyword(s):  
Food Chain ◽  
Complex Dynamics ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Chain Model ◽  
Narrow Region ◽  
Type Iv ◽  
Numerical Bifurcation ◽  
Parameter Values ◽  
Food Chain Model

In this paper, dynamical complexities of a three species food chain model with Holling type IV predator response is investigated analytically as well as numerically. The local and global stability analysis is carried out. The persistence criterion of the food chain model is obtained. Numerical bifurcation analysis reveals the chaotic behavior in a narrow region of the bifurcation parameter space for biologically realistic parameter values of the model system. Transition to chaotic behavior is established via period-doubling bifurcation and some sequences of distinctive period-halving bifurcation leading to limit cycles are observed.

Stability and Bifurcation Analysis in a Food Chain Model with Delay

2011 ◽  
Vol 110-116 ◽  
pp. 3382-3388
Author(s):  
Zhang Li
Keyword(s):  
Hopf Bifurcation ◽  
Food Chain ◽  
Center Manifold ◽  
Chain Model ◽  
Center Manifold Theory ◽  
Stability And Bifurcation Analysis ◽  
Existence And Stability ◽  
The Stability ◽  
Manifold Theory ◽  
Food Chain Model

In this paper, we investigate a delayed three-species food chain model. The existence and stability of equilibria are obtained. A explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form and the center manifold theory.

scholarly journals Complex dynamics in a tritrophic food chain model with general functional response

2020 ◽  
Vol 33 (2) ◽  
Author(s):  
Mohammed Y. Dawed ◽  
Patrick M. Tchepmo Djomegni ◽  
Harald E. Krogstad
Keyword(s):  
Functional Response ◽  
Food Chain ◽  
Complex Dynamics ◽  
Chain Model ◽  
Food Chain Model

DIFFUSIVE INSTABILITY AND TRAVELING WAVES IN A MANGROVE ECOSYSTEM FOOD-CHAIN MODEL WITH DELAYED DETRITUS RECYCLING

2010 ◽  
Vol 03 (02) ◽  
pp. 225-241 ◽  
Author(s):  
B. MUKHOPADHYAY ◽  
ASHOKE BERA ◽  
R. BHATTACHARYYA
Keyword(s):  
Traveling Waves ◽  
Food Chain ◽  
Homogeneous System ◽  
Mangrove Ecosystem ◽  
Travelling Wave ◽  
Chain Model ◽  
Travelling Wave Solutions ◽  
Interaction Rate ◽  
The Stability ◽  
Food Chain Model

In this paper, a food-chain model in a mangrove ecosystem with detritus recycling is analyzed. From the stability analysis of the delayed homogeneous system, an interval for the parameter representing detritus-detritivores interaction rate is obtained that imparts stability to the system around the coexistent state. Next, we have studied the model in a nonhomogeneous environment. The analysis revealed the existence of a subinterval of the above mentioned interval such that when the above interaction-rate lies within this interval, the system will undergo diffusion driven instability. Finally, we show the existence of travelling wave solutions for the said ecosystem. Numerical simulations are carried out to augment analytical results.

Stability and Bifurcation Analysis of a Three-Species Food Chain Model with Fear

2018 ◽  
Vol 28 (01) ◽  
pp. 1850009 ◽  
Author(s):  
Pijush Panday ◽  
Nikhil Pal ◽  
Sudip Samanta ◽  
Joydev Chattopadhyay
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Bifurcation Analysis ◽  
Food Chain ◽  
Limit Cycles ◽  
Equilibrium Analysis ◽  
Chain Model ◽  
Maximum Lyapunov Exponent ◽  
The Cost ◽  
Food Chain Model

In the present paper, we investigate the impact of fear in a tri-trophic food chain model. We propose a three-species food chain model, where the growth rate of middle predator is reduced due to the cost of fear of top predator, and the growth rate of prey is suppressed due to the cost of fear of middle predator. Mathematical properties such as equilibrium analysis, stability analysis, bifurcation analysis and persistence have been investigated. We also describe the global stability analysis of the equilibrium points. Our numerical simulations reveal that cost of fear in basal prey may exhibit bistability by producing unstable limit cycles, however, fear in middle predator can replace unstable limit cycles by a stable limit cycle or a stable interior equilibrium. We observe that fear can stabilize the system from chaos to stable focus through the period-halving phenomenon. We conclude that chaotic dynamics can be controlled by the fear factors. We apply basic tools of nonlinear dynamics such as Poincaré section and maximum Lyapunov exponent to identify the chaotic behavior of the system.

Sign in / Sign up

Export Citation Format

Share Document