Title :
A route to chaos with a chain of homoclinic bifurcations in a modified Bonhoffer-van der Pol equation
Author :
Tsumoto, Kunichika ; Yoshinaga, Tetsuya ; Kawakami, Hiroshi
Author_Institution :
Fac. of Eng., Tokushima Univ., Japan
Abstract :
We survey a mechanism of a route to chaos due to a successive bifurcation process including a chain of homoclinic bifurcations observed in a modified Bonhoffer-van der Pol equation. The occurrence of homoclinic bifurcations is confirmed by using the linking number of limit cycles related with the stable manifold through an equilibrium
Keywords :
bifurcation; chaos; circuit oscillations; differential equations; limit cycles; autonomous differential equation; burst oscillations; dynamical systems; electrical circuit; homoclinic bifurcations; limit cycles; modified Bonhoffer van der Pol equation; neurons; rectangular waveform; route to chaos; stable manifold; successive bifurcation process; Bifurcation; Biomedical engineering; Chaos; Chemicals; Circadian rhythm; Circuits; Density estimation robust algorithm; Joining processes; Limit-cycles; Nonlinear equations;
Conference_Titel :
Industrial Electronics Society, 2000. IECON 2000. 26th Annual Confjerence of the IEEE
Conference_Location :
Nagoya
Print_ISBN :
0-7803-6456-2
DOI :
10.1109/IECON.2000.972594
