A dynamical system with Hopf bifurcations and catastrophes

DOI10.1016/0096-3003(89)90036-2zbMath0663.92017OpenAlexW2093300296MaRDI QIDQ1115375

Sergio Rinaldi, Simona Muratori

Publication date: 1989

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0096-3003(89)90036-2

zbMATH Keywords

limit cycleHopf bifurcationstable equilibriumsteady statefood chainprey-predator modelperiodic statecatastrophes of fold typehysterese phenomenarenewable sourcesecond-order positive dynamic system

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Population dynamics (general) (92D25) Ecology (92D40) Control/observation systems governed by ordinary differential equations (93C15) Catastrophe theory (58K35) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (7)

A separation condition for the existence of limit cycles in slow-fast systems ⋮ Bifurcation analysis of two predator-prey models ⋮ Remarks on food chain dynamics ⋮ Homoclinic bifurcations in slow-fast second order systems ⋮ Catastrophic bifurcations in a second-order dynamical system with application to acid rain and forest collapse ⋮ Limit cycles in slow-fast forest-pest models ⋮ Analytical study of a triple Hopf bifurcation in a tritrophic food chain model

Cites Work

• Stability analysis of predator-prey models via the Liapunov method
• The dynamics of two interacting populations
• Uniqueness of a Limit Cycle for a Predator-Prey System
• The Interaction of Steady State and Hopf Bifurcations in a Two-Predator–One-Prey Competition Model
• Competing Predators
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