Related papers: Early warning signals for desynchronization in per…
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…
Synchronization is central to many complex systems in engineering physics (e.g., the power-grid, Josephson junction circuits, and electro-chemical oscillators) and biology (e.g., neuronal, circadian, and cardiac rhythms). Despite these…
We consider a model for substrate-depletion oscillations in genetic systems, based on a stochastic differential equation with a slowly evolving external signal. We show the existence of critical transitions in the system. We apply two…
Many natural systems undergo critical transitions, i.e. sudden shifts from one dynamical regime to another. In the climate system, the atmospheric boundary layer can experience sudden transitions between fully turbulent states and…
Synchronization is an important phenomenon in a wide variety of systems comprising interacting oscillatory units, whether natural (like neurons, biochemical reactions, cardiac cells) or artificial (like metronomes, power grids, Josephson…
Accurately detecting drowsiness is vital to driving safety. Among all measures, physiological-signal-based drowsiness monitoring can be more privacy-preserving than a camera-based approach. However, conflicts exist regarding how…
Nonlinear dynamical systems with time delay are abundant in applications, but are notoriously difficult to analyse and predict because delay-induced effects strongly depend on the form of the nonlinearities involved, and on the exact way…
We study the effects of noise on the dynamics of a system of coupled self-propelling particles in the case where the coupling is time-delayed, and the delays are discrete and randomly generated. Previous work has demonstrated that the…
The cooperative behavior of neurons and neuronal areas associated with the synchronization behavior proves to be a fundamental neural mechanism. In addition, abnormal levels of synchronization have been related to unhealthy neural…
Circadian oscillation provides selection advantages through synchronization to the daylight cycle. However, a reliable clock must be designed through two conflicting properties: entrainability to synchronize internal time with periodic…
We show that the unavoidable increase in neuronal response latency to ongoing stimulation serves as a nonuniform gradual stretching of neuronal circuit delay loops and emerges as an essential mechanism in the formation of various types of…
Synchronization is ubiquitous in nature, which is mathematically described by coupled oscillators. Synchronization strongly depends on the interaction network, and the network plays a crucial role in controlling the dynamics. To understand…
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…
We study a system of coupled phase oscillators near a saddle-node on an invariant circle bifurcation and driven by random intrinsic frequencies. Under the variation of control parameters, the system undergoes a phase transition changing the…
We consider a heteroclinic network in the framework of winnerless competition of species. It consists of two levels of heteroclinic cycles. On the lower level, the heteroclinic cycle connects three saddles, each representing the survival of…
Heteroclinic cycles are widely used in neuroscience in order to mathematically describe different mechanisms of functioning of the brain and nervous system. Heteroclinic cycles and interactions between them can be a source of different…
Time lags occur in a vast range of real-world dynamical systems due to finite reaction times or propagation speeds. Here we derive an analytical approach to determine the asymptotic stability of synchronous states in networks of coupled…
Critical transitions in multistable systems have been discussed as models for a variety of phenomena ranging from the extinctions of species to socio-economic changes and climate transitions between ice-ages and warm-ages. From bifurcation…
Predicting the occurrence of transitions in the qualitative dynamics of many natural systems is crucial, yet it remains a challenging task. Generic early warning signals like variance and lag-1 autocorrelation identify critical slowing down…
We explore sequential escape behaviour of coupled bistable systems under the influence of stochastic perturbations. We consider transient escapes from a marginally stable "quiescent" equilibrium to a more stable "active" equilibrium. The…