Homoclinic bifurcations in slow-fast second order systems

[1]  É. Benoît.  Chasse au canard , 1980 .

[2]  Yu. A. Kuznetsov.  Computation of Invariant Manifold Bifurcations , 1990 .

[3]  Kuo-Shung Cheng,et al.  UNIQUENESS OF A LIMIT CYCLE FOR A PREDATOR-PREY SYSTEM* , 1981 .

[4]  Mark J. Friedman,et al.  Numerical computation and continuation of invariant manifolds connecting fixed points , 1991 .

[5]  C. S. Holling,et al.  The functional response of predators to prey density and its role in mimicry and population regulation. , 1965 .

[6]  A. Hastings,et al.  Chaos in a Three-Species Food Chain , 1991 .

[7]  S. Muratori.  An application of the separation principle for detecting slow-fast limit cycles in a three-dimensional system , 1991 .

[8]  A. Spence,et al.  Continuation and Bifurcations: Numerical Techniques and Applications , 1990 .

[9]  Stephen Schecter,et al.  Persistent unstable equilibria and closed orbits of a singularly perturbed equation , 1985 .

[10]  D M Wrzosek,et al.  Limit cycles in predator-prey models. , 1990, Mathematical biosciences.

[11]  S. Rinaldi,et al.  A dynamical system with Hopf bifurcations and catastrophes , 1989 .

[12]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[13]  P. Holmes,et al.  New Approaches to Nonlinear Problems in Dynamics , 1981 .

[14]  Sergio Rinaldi,et al.  Low- and high-frequency oscillations in three-dimensional food chain systems , 1992 .

[15]  F. Hoppensteadt.  Asymptotic stability in singular perturbation problems , 1968 .

[16]  Brian D. Hassard.  Computation of invariant manifolds , 1980 .

[17]  Peter Szmolyan,et al.  Transversal heteroclinic and homoclinic orbits in singular perturbation problems , 1991 .

[18]  A. Zvonkin,et al.  Non-standard analysis and singular perturbations of ordinary differential equations , 1984 .

[19]  Sergio Rinaldi,et al.  A separation condition for the existence of limit cycles in slow-fast systems , 1991 .

[20]  F. Hoppensteadt.  Asymptotic stability in singular perturbation problems. II: Problems having matched asymptotic expansion solutions☆ , 1974 .

[21]  Marten Scheffer,et al.  Fish and nutrients interplay determines algal biomass : a minimal model , 1991 .

[22]  Sergio Rinaldi,et al.  Slow-fast limit cycles in predator-prey models , 1992 .

[23]  Marten Scheffer,et al.  Should we expect strange attractors behind plankton dynamics―and if so, should we bother? , 1991 .