Dynamics in a discrete-time predator-prey system with Allee effect

DOI10.1007/s10255-013-0207-5zbMath1269.37035OpenAlexW1985826620WikidataQ115605883 ScholiaQ115605883MaRDI QIDQ1945979

Zhu-jun Jing, Xiang-Ling Fu, Xian-Wei Chen

Publication date: 17 April 2013

Published in: Acta Mathematicae Applicatae Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10255-013-0207-5

zbMATH Keywords

Hopf bifurcationtransient chaosperiodic windowpredator-prey systemflip bifurcationAllee effectMarotto's chaosinvariant circle

Mathematics Subject Classification ID

Dynamical systems in biology (37N25) Numerical chaos (65P20) Numerical bifurcation problems (65P30)

Related Items (17)

Dynamics of a discrete-time predator-prey system ⋮ Derivation and analysis of a discrete predator-prey model ⋮ Codimension-3 Flip Bifurcation of a Class of Difference Equations ⋮ Codimension-Two Bifurcations and Bifurcation Controls in a Discrete Biological System with Weak Allee Effect ⋮ Complex dynamics in a discrete-time predator-prey system without Allee effect ⋮ Dynamics in a discrete time model of logistic type ⋮ Bifurcation and chaos of a nonlinear discrete-time predator-prey model involving the nonlinear Allee effect ⋮ ALLEE EFFECT IN A RICKER TYPE DISCRETE-TIME PREDATOR–PREY MODEL WITH HOLLING TYPE-II FUNCTIONAL RESPONSE ⋮ Bifurcation and chaos in a discrete-time predator-prey system of Holling and Leslie type ⋮ Stability and bifurcation of a discrete predator-prey system with Allee effect and other food resource for the predators ⋮ Neimark-Sacker bifurcation in a tritrophic model with defense in the prey ⋮ Bifurcation analysis and chaos control in a discrete epidemic system ⋮ Unnamed Item ⋮ Persistence and stability analysis of discrete-time predator–prey models: a study of population and evolutionary dynamics ⋮ Chaos control in a discrete-time predator–prey model with weak Allee effect ⋮ Persistence of a discrete-time predator-prey model with stage-structure in the predator ⋮ Long-term dynamics of discrete-time predator–prey models: stability of equilibria, cycles and chaos

Cites Work

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• Allee effect in a discrete-time predator-prey system
• Allee effects on population dynamics in continuous (overlapping) case
• Bifurcation and chaos in discrete\,-\,time predator\,-\,prey system
• Allee effects on population dynamics with delay
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Preturbulence: A regime observed in a fluid flow model of Lorenz
• Snap-back repellers imply chaos in \(\mathbb{R}^n\)
• Nonlinear stiffness, Lyapunov exponents, and attractor dimension
• Allee effect in a prey-predator system
• Complex dynamic behaviors of a discrete-time predator-prey system
• On redefining a snap-back repeller
• Allee effects in a discrete-time host-parasitoid model

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