Synthesizing attractors of Hindmarsh-Rose neuronal systems

Marius-F. Danca (1, 2) , Qingyun Wang (3, 4)

1 Dept. of Mathematics and Computer Science
2 Romanian Institute of Science and Technology
3 Dept. of Dynamics and Control
4 School of Statistics and Mathematics

In this paper a periodic parameter-switching scheme is applied to the Hindmarsh-Rose neuronal system to synthesize certain attractors. Results show numerically, via computer graphic simulations, that the obtained synthesized attractor belongs to the class of all admissible attractors for the Hindmarsh-Rose neuronal system and matches the averaged attractor obtained with the control parameter replaced with the averaged switched parameter values. This feature allows us to imagine that living beings are able to maintain vital behavior while the control parameter switches so that their dynamical behavior is suitable for the given environment.

Mots clés: Hindmarsh-Rose model; Chaotic attractors; Local attractors; Global attractors

Marius-F. Danca, Qingyun Wang. Synthesizing attractors of Hindmarsh-Rose neuronal systems. Nonlinear Dynamics, 2010, 62 (1-2), pp.437-446. ⟨10.1007/s11071-010-9730-6⟩. ⟨hal-00593404⟩