Nonlocal branches of cycles, bistability, and topologically persistent mixed mode oscillations.
A possible mechanism for generating mixed mode oscillations is based on an appropriate S-shaped structure, which graphs the relation between the parameter and the collection of periodic oscillations existing for a particular parameter value in the product of parameter and phase spaces. This natural scenario should be supplemented by simple and constructive criteria of existence, and methods of localization, of such S-shaped structures. These criteria are the main focus of the paper.
Bouse
E
E
Department of Applied Mathematics, University College Cork, Cork, Ireland.
Krasnosel'skii
A
A
Pokrovskii
A
A
Rachinskii
D
D
D000465:Algorithms; D001683:Biological Clocks / Q000502:physiology*; D003198:Computer Simulation; D005246:Feedback / Q000502:physiology*; D008954:Models, Biological; D017711:Nonlinear Dynamics