Bulg. J. Phys. vol.38 no.3 (2011), pp. 303-308

Desynchronization of Systems of Coupled Hindmarsh-Rose Oscillators

A. Gjurchinovski1, V. Urumov1, Z. Vasilkoski2
1Institute of Physics, Faculty of Natural Sciences and Mathematics, Sts. Cyril and Methodius University, P.O. Box 162, 1000 Skopje, Macedonia
2Harvard Medical School, Goldenson 343, Boston, MA 02115, USA
Abstract. It is widely assumed that neural activity related to synchronous rhythms of large portions of neurons in specific locations of the brain is responsible for the pathology manifested in patients' uncontrolled tremor and other similar diseases. To model such systems Hindmarsh-Rose (HR) oscillators are considered as appropriate as they mimic the qualitative behaviour of neuronal firing. Here we consider a large number of identical HR-oscillators interacting through the mean field created by the corresponding components of all oscillators. Introducing additional coupling by feedback of Pyragas type, proportional to the difference between the current value of the mean-field and its value some time in the past, Rosenblum and Pikovsky (Phys. Rev. E 70, 041904, 2004) demonstrated that the desirable desynchronization could be achieved with appropriate set of parameters for the system. Following our experience with stabilization of unstable steady states in dynamical systems, we show that by introducing a variable delay, desynchronization is obtainable for much wider range of parameters and that at the same time it becomes more pronounced.

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