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.

scholarly journals Travelling Waves of an n-Species Food Chain Model with Spatial Diffusion and Time Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Fei Hu ◽  
Yuyin Xu ◽  
Z. Wang ◽  
Wei Ding
Keyword(s):  
Fixed Point ◽  
Food Chain ◽  
Time Delays ◽  
Travelling Waves ◽  
Travelling Wave ◽  
Spatial Diffusion ◽  
Chain Model ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Food Chain Model

We investigate an n-species food chain model with spatial diffusion and time delays. By using Schauder’s fixed point theorem, we obtain the result about the existence of the travelling wave solutions of the food chain model with reaction term satisfying the partial quasimonotonicity conditions.

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

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.

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.

Spatial patterns created by cross-diffusion for a three-species food chain model

2014 ◽  
Vol 07 (02) ◽  
pp. 1450013 ◽  
Author(s):  
Canrong Tian ◽  
Zhi Ling ◽  
Zhigui Lin
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Spatial Patterns ◽  
Food Chain ◽  
Turing Instability ◽  
Steady States ◽  
Chain Model ◽  
Cross Diffusion ◽  
The Stability ◽  
Food Chain Model

This paper deals with the stability analysis to a three-species food chain model with cross-diffusion, the results of which show that there is no Turing instability but cross-diffusion makes the model instability possible. We then show that the spatial patterns are spotted patterns by using numerical simulations. In order to understand why the spatial patterns happen, the existence of the nonhomogeneous steady states is investigated. Finally, using the Leray–Schauder theory, we demonstrate that cross-diffusion creates nonhomogeneous stationary patterns.

scholarly journals Chaos in Beddington–DeAngelis food chain model with fear

2020 ◽  
Vol 1591 ◽  
pp. 012082
Author(s):  
Hiba Abdullah Ibrahim ◽  
Raid Kamel Naji
Keyword(s):  
Food Chain ◽  
Chain Model ◽  
Food Chain Model
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