Homoclinic bifurcations in slow-fast second order systems

Nonlinear Analysis

Volumn 25, Issue 7, 1995, Pages 747-762

  Kuznetsov, Yuri A ^a,b   Muratori, Simona ^a,b   Rinaldi, Sergio ^b  

^a CWI   (Netherlands)

^b POLITECNICO DI MILANO   (Italy)

Author keywords

continuation method.; Homoclinic bifurcations; predatorprey models; singular perturbation

Indexed keywords

EID: 0010427610     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/0362-546X(94)E0005-2     Document Type: Article

References (28)

1. Bifurcation theory
2. Transversal heteroclinic and homoclinic orbits in singular perturbation problems
3. Asymptotic stability in singular perturbation problems
4. Non-standard analysis and singular perturbations of ordinary differential equations
5. Systems of differential equations containing small parameters at derivatives
6. Asymptotic behavior of solutions of systems of differential equations with a small parameter at higher derivatives
7. Persistent unstable equilibria and closed orbits of singularly perturbed equations
8. Chasse au canards
9. Slow-fast limit cycles in preadatorprey models
10. Sept formules relatives aux canards
11. Fish and nutrients interplay determines algal biomass
12. The functional response of predators to prey density and its role in mimicry and population regulation
13. Limit cycles in predatorprey communities
14. Uniqueness of a limit cycle for a predatorprey system
15. Limit cycles in predatorprey models
16. A dynamical system with Hopf bifurcations and catastrophes
17. Should we expect strange attractors behind plankton dynamics and if so, should we bother?
18. Chaos in a three species food chain
19. An application of the separation principle for detecting slow-fast limit cycles in a three-dimensional system
20. A separation condition for the existence of limit cycles in slow-fast systems
21. Low and high frequency oscillations in three dimensional food chain systems
22. Global bifurcations and their numerical comnputations
23. Numerical computation and continuation of invariant manifolds connecting fixed points
24. Computation of invariant manifolds