Related papers: Desynchronization of systems of coupled Hindmarsh-…
Synchronization is a ubiquitous phenomenon in nature. Although it is necessary for the functioning of many systems, too much synchronization can also be detrimental, e.g., (partially) synchronized brain patterns support high-level cognitive…
In this paper, we address the reduced-order synchronization problem between two chaotic memristive Hindmarsh-Rose (HR) neurons of different orders using two distinct methods. The first method employs the Lyapunov active control technique.…
A biophysical model of arousal dynamics is used to study mechanisms of synchronisation and loss of synchrony among the three key oscillators controlling sleep-wake cycles: the circadian, homeostatic, and light oscillators. Synchronisation…
Neural synchronization is believed to be critical for many brain functions. It frequently exhibits temporal variability, but it is not known if this variability has a specific temporal patterning. This study explores these…
In this contribution, we have considered the collective behavior of the two as well as the network of heterogeneous coupled Hindmarsh Rose (HR) neurons. The heterogeneous models were made of a memristive 2D (HR) and the traditional 3D HR…
Based on the invariance principle of differential equations a simple, systematic, and rigorous feedback scheme with the variable feedback strength is proposed to stabilize nonlinearly any chaotic systems without any prior analytical…
Motivated by deep brain stimulation treatment of neural disorders such as Parkinson's disease, it has been proposed that desynchronization of neural oscillators can be achieved by maximizing the Lyapunov exponent of the phase difference…
The synchronized activity of neuronal populations can lead to pathological over-synchronization in conditions such as epilepsy and Parkinson disease. Such states can be desynchronized by brief electrical pulses. But when the underlying…
A universal approach is proposed for suppression of collective synchrony in a large population of interacting rhythmic units. We demonstrate that provided that the internal coupling is weak, stabilization of overall oscillations with…
In large-scale neural networks, coherent limit cycle oscillations usually coexist with unstable incoherent equilibrium states, which are not observed experimentally. We implement a first-order dynamic controller to stabilize unknown…
Suppression of excessively synchronous beta-band oscillatory activity in the brain is believed to suppress hypokinetic motor symptoms of Parkinson's disease. Recently, a lot of interest has been devoted to desynchronizing delayed feedback…
Synchronization of coupled dynamical systems is a widespread phenomenon in both biological and engineered networks, and understanding this behavior is crucial for controlling such systems. Considerable research has been dedicated to…
Synchronization of coupled oscillators is observed in many natural and engineered systems and emerges due to the interactions within the system. It can be both beneficial, e.g., in power grids, and harmful, e.g., in epileptic seizures. In…
Dissipative coupling is known to induce synchronization. Conversely it may be hypothesized that oscillators driven to synchronize may reduce power dissipation in their coupling. The latter scenario is realized in the human cardiorespiratory…
Understanding complex systems which exhibit desynchronization as an emergent property should have important implications, particularly in treating neurological disorders and designing efficient communication networks. Here were demonstrate…
We discuss synchronization in networks of neuronal oscillators which are interconnected via diffusive coupling, i.e. linearly coupled via gap junctions. In particular, we present sufficient conditions for synchronization in these networks…
The use of spikes to carry information between brain areas implies complete or partial synchronization of the neurons involved. The degree of synchronization reached by two coupled systems and the energy cost of maintaining their…
By a small-size complex network of coupled chaotic Hindmarsh-Rose circuits, we study experimentally the stability of network synchronization to the removal of shortcut links. It is shown that the removal of a single shortcut link may…
We have identified the occurrence of chimera states for various coupling schemes in networks of two-dimensional and three-dimensional Hindmarsh-Rose oscillators, which represent realistic models of neuronal ensembles. This result, together…
A new model of two coupled neurons is presented by the partly diffusive Hindmarsh-Rose equations. The solution semiflow exhibits globally absorbing characteristics. As the main result, the self-synchronization of the coupled neurons at a…