Homoclinic bifurcations in slow-fast second order systems
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Publication:4855163
DOI10.1016/0362-546X(94)E0005-2zbMath0840.34065OpenAlexW1979864406MaRDI QIDQ4855163
Sergio Rinaldi, Simona Muratori, Yuri A. Kuznetsov
Publication date: 9 July 1996
Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0362-546x(94)e0005-2
bifurcationLotka-Volterra-systemsingular homoclinic orbittwo-dimensional singularly perturbed autonomous differential system
Singular perturbations for ordinary differential equations (34E15) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)
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Cites Work
- An application of the separation principle for detecting slow-fast limit cycles in a three-dimensional system
- Transversal heteroclinic and homoclinic orbits in singular perturbation problems
- Limit cycles in predator-prey models
- Persistent unstable equilibria and closed orbits of a singularly perturbed equation
- A dynamical system with Hopf bifurcations and catastrophes
- Limit cycles in slow-fast forest-pest models
- Asymptotic stability in singular perturbation problems. II: Problems having matched asymptotic expansion solutions
- A separation condition for the existence of limit cycles in slow-fast systems
- Non-standard analysis and singular perturbations of ordinary differential equations
- Uniqueness of a Limit Cycle for a Predator-Prey System
- Numerical Computation and Continuation of Invariant Manifolds Connecting Fixed Points
- Low- and High-Frequency Oscillations in Three-Dimensional Food Chain Systems
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