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.

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.

On the explosive instability in a three-species food chain model with modified Holling type IV functional response

2017 ◽  
Vol 40 (16) ◽  
pp. 5707-5726 ◽  
Author(s):  
Rana D. Parshad ◽  
Ranjit Kumar Upadhyay ◽  
Swati Mishra ◽  
Satish Kumar Tiwari ◽  
Swarnali Sharma
Keyword(s):  
Functional Response ◽  
Food Chain ◽  
Chain Model ◽  
Explosive Instability ◽  
Type Iv ◽  
Food Chain Model

Fear Effect in a Tri-Trophic Food Chain Model with Holling Type IV Functional Response

2021 ◽  
Vol 9 (3) ◽  
Author(s):  
Krishnendu Sarkar ◽  
Nijamuddin Ali ◽  
Lakshmi Narayan Guin
Keyword(s):  
Functional Response ◽  
Food Chain ◽  
Chain Model ◽  
Type Iv ◽  
Fear Effect ◽  
Food Chain Model

scholarly journals Chaotic Discrete Fractional-Order Food Chain Model and Hybrid Image Encryption Scheme Application

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 161
Author(s):  
Sameh Askar ◽  
Abdulrahman Al-khedhairi ◽  
Amr Elsonbaty ◽  
Abdelalim Elsadany
Keyword(s):  
Fractional Order ◽  
Food Chain ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
High Sensitivity ◽  
Phase Portraits ◽  
Chain Model ◽  
Encryption Scheme ◽  
Dynamical Behaviors ◽  
Food Chain Model

Using the discrete fractional calculus, a novel discrete fractional-order food chain model for the case of strong pressure on preys map is proposed. Dynamical behaviors of the model involving stability analysis of its equilibrium points, bifurcation diagrams and phase portraits are investigated. It is demonstrated that the model can exhibit a variety of dynamical behaviors including stable steady states, periodic and quasiperiodic dynamics. Then, a hybrid encryption scheme based on chaotic behavior of the model along with elliptic curve key exchange scheme is proposed for colored plain images. The hybrid scheme combines the characteristics of noise-like chaotic dynamics of the map, including high sensitivity to values of parameters, with the advantages of reliable elliptic curves-based encryption systems. Security analysis assures the efficiency of the proposed algorithm and validates its robustness and efficiency against possible types of attacks.

On the Integrability and Chaotic Behavior of an Ecological Model

1997 ◽  
Vol 07 (02) ◽  
pp. 463-468 ◽  
Author(s):  
M. P. Joy
Keyword(s):  
Bifurcation Diagram ◽  
Lyapunov Exponents ◽  
Food Chain ◽  
Ecological Model ◽  
Chaotic Behavior ◽  
Painlevé Analysis ◽  
Chain Model ◽  
Numerical Techniques ◽  
Food Chain Model ◽  
Painleve Analysis

A three-species food chain model is studied analytically as well as numerically. Integrability of the model is studied using Painlevé analysis while chaotic behavior is studied using numerical techniques, such as calculation of Lyapunov exponents, plotting the bifurcation diagram and phase plots. We correct and critically comment on the wrong results reported recently on this ecological model, in a paper by Rai "1995".

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.

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

scholarly journals Chaos in a Hybrid Food Chain Model

2021 ◽  
pp. 2362-2368
Author(s):  
Safaa Jawad Ali ◽  
Abed Almohsen Naji Almohasin ◽  
Adwea Naji Atewi ◽  
Raid Kamel Naji ◽  
Norihan Md Arifin
Keyword(s):  
Global Stability ◽  
Food Chain ◽  
Direct Method ◽  
Equilibrium Points ◽  
Chain Model ◽  
Lyapunov Direct Method ◽  
Type Iv ◽  
Controlling Parameter ◽  
Periodic Dynamics ◽  
Food Chain Model

In this paper, chaotic and periodic dynamics in a hybrid food chain system with Holling type IV and Lotka-Volterra responses are discussed. The system is observed to be dissipative. The global stability of the equilibrium points is analyzed using Routh-Hurwitz criterion and Lyapunov direct method. Chaos phenomena is characterized by attractors and bifurcation diagram. The effect of the controlling parameter of the model is investigated theoretically and numerically.

BIFURCATION AND PREDICTABILITY ANALYSIS OF A LOW-ORDER ATMOSPHERIC CIRCULATION MODEL

1995 ◽  
Vol 05 (06) ◽  
pp. 1701-1711 ◽  
Author(s):  
A. SHIL'NIKOV ◽  
G. NICOLIS ◽  
C. NICOLIS
Keyword(s):  
Atmospheric Circulation ◽  
Complex Dynamics ◽  
Chaotic Behavior ◽  
Winter Season ◽  
Period Doubling ◽  
Circulation Model ◽  
Predictability Analysis ◽  
Parameter Ranges ◽  
Parameter Values ◽  
Low Order

A comprehensive bifurcation analysis of a low-order atmospheric circulation model is carried out. It is shown that the model admits a codimension-2 saddle-node-Hopf bifurcation. The principal mechanisms leading to the appearance of complex dynamics around this bifurcation are described and various routes to chaotic behavior are identified, such as the transition through the period doubling cascade, the breakdown of an invariant torus and homoclinic bifurcations of a saddle-focus. Non-trivial limit sets in the form of a chaotic attractor or a chaotic repeller are found in some parameter ranges. Their presence implies an enhanced unpredictability of the system for parameter values corresponding to the winter season.

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