Macro- and micro-chaotic structures in the Hindmarsh-Rose model of bursting neurons
- Computational Dynamics Group, Departamento de Matemática Aplicada, GME and IUMA, Universidad de Zaragoza, E-50009 Zaragoza (Spain)
- Computational Dynamics Group, GME, Universidad de Zaragoza, E-50009 Zaragoza (Spain)
- Neuroscience Institute and Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia 30078 (United States)
We study a plethora of chaotic phenomena in the Hindmarsh-Rose neuron model with the use of several computational techniques including the bifurcation parameter continuation, spike-quantification, and evaluation of Lyapunov exponents in bi-parameter diagrams. Such an aggregated approach allows for detecting regions of simple and chaotic dynamics, and demarcating borderlines—exact bifurcation curves. We demonstrate how the organizing centers—points corresponding to codimension-two homoclinic bifurcations—along with fold and period-doubling bifurcation curves structure the biparametric plane, thus forming macro-chaotic regions of onion bulb shapes and revealing spike-adding cascades that generate micro-chaotic structures due to the hysteresis.
- OSTI ID:
- 22351116
- Journal Information:
- Chaos (Woodbury, N. Y.), Vol. 24, Issue 2; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 1054-1500
- Country of Publication:
- United States
- Language:
- English
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