Stability and bifurcations analysis in an ecoepidemic system with prey group defense and two infectious routes

AbstractA model for predator-prey interactions with herd behaviour is proposed. Novelty includes a smooth transition from individual behaviour (low number of prey) to herd behaviour (large number of prey). The model is analysed using standard stability and bifurcations techniques. We prove that the system undergoes a Hopf bifurcation as we vary the parameter that represents the efficiency of predators (dependent on the predation rate, for instance), giving rise to sustained oscillations in the system. The proposed model appears to possess more realistic features than the previous approaches while being also relatively easier to analyse and understand.

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Bifurcation Analysis of a Delay-Induced Predator–Prey Model with Allee Effect and Prey Group Defense

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127421501583 ◽

2021 ◽

Vol 31 (10) ◽

pp. 2150158

Author(s):

Yong Ye ◽

Yi Zhao

Keyword(s):

Hopf Bifurcation ◽

Bifurcation Analysis ◽

Allee Effect ◽

Periodic Oscillation ◽

Predator Prey ◽

Predator Prey Model ◽

Prey Group ◽

Prey Model ◽

Group Defense ◽

The Stability

In this paper, we establish a predator–prey model with focus on the Allee effect and prey group defense. The positivity and boundedness of the model, existence of equilibrium point, and stability change caused by Allee effect are studied. Bifurcation (transcritical bifurcation, Hopf bifurcation) analysis is discussed, and the direction of Hopf bifurcation is determined by calculating the first Lyapunov number. Then we introduce delay into the original model and consider the influence of delay on the stability of the model. By selecting delay as the bifurcation parameter, we obtain the existence conditions of Hopf bifurcation and the direction of Hopf bifurcation. Finally, we verify the theoretical analysis by numerical simulation. Considering both the Allee effect and the prey group defense, the dynamic behavior near the origin becomes more complex than only considering Allee effect or prey group defense in the model. Allee effect can bring the risk of extinction and the change of stability, and the delay effect can make the stable coexistence equilibrium unstable and lead to periodic oscillation.

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An ecoepidemic model with diseased predators and prey group defense

Simulation Modelling Practice and Theory ◽

10.1016/j.simpat.2013.02.004 ◽

2013 ◽

Vol 34 ◽

pp. 144-155 ◽

Cited By ~ 17

Author(s):

Sabrina Belvisi ◽

Ezio Venturino

Keyword(s):

Prey Group ◽

Group Defense

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Natural convection in a rectangular cavity with piece-wise heated vertical walls: multiple states, stability and bifurcations

10.1615/ihtc12.60 ◽

2002 ◽

Cited By ~ 1

Author(s):

Vladimir Erenburg ◽

Alexander Gelfgat ◽

Eliezer Kit ◽

Pinhas Z. Bar-Yoseph ◽

Alexander Solan

Keyword(s):

Natural Convection ◽

Rectangular Cavity ◽

Vertical Walls ◽

Stability And Bifurcations

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Global Stability Analysis of a Bioreactor Model for Phenol and Cresol Mixture Degradation

Processes ◽

10.3390/pr9010124 ◽

2021 ◽

Vol 9 (1) ◽

pp. 124

Author(s):

Neli Dimitrova ◽

Plamena Zlateva

Keyword(s):

Specific Growth ◽

Equilibrium Points ◽

Nonlinear Ordinary Differential Equations ◽

The Novel ◽

Model Design ◽

Stirred Bioreactor ◽

Global Stability Analysis ◽

Local Asymptotic Stability ◽

Model Dynamics ◽

Stability And Bifurcations

We propose a mathematical model for phenol and p-cresol mixture degradation in a continuously stirred bioreactor. The model is described by three nonlinear ordinary differential equations. The novel idea in the model design is the biomass specific growth rate, known as sum kinetics with interaction parameters (SKIP) and involving inhibition effects. We determine the equilibrium points of the model and study their local asymptotic stability and bifurcations with respect to a practically important parameter. Existence and uniqueness of positive solutions are proved. Global stabilizability of the model dynamics towards equilibrium points is established. The dynamic behavior of the solutions is demonstrated on some numerical examples.

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