Related papers: Early warning signal for interior crises in excita…

The analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations comprised of $N$ stochastic excitable units each is performed by studying an approximate system, obtained by…

Networks of excitable nodes have recently attracted much attention particularly in regards to neuronal dynamics, where criticality has been argued to be a fundamental property. Refractory behavior, which limits the excitability of neurons…

This paper studies a stylized model of local interaction where agents choose from an ever increasing set of vertically ranked actions, e.g. technologies. The driving forces of the model are infrequent upward shifts (``updates''), followed…

Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant Lyapunov vectors have been proposed as…

We consider stochastic electro-mechanical dynamics of an overdamped power system in the vicinity of the saddle-node bifurcation associated with the loss of global stability such as voltage collapse or phase angle instability. Fluctuations…

An extremely challenging problem of significant interest is to predict catastrophes in advance of their occurrences. We present a general approach to predicting catastrophes in nonlinear dynamical systems under the assumption that the…

Conditions such as insomnia, cardiac arrhythmia and jet-lag share a common feature: they are all related to the ability of biological systems to synchronize with the day-night cycle. When organisms lose resilience, this ability of…

This paper investigates biological models that represent the transition equation from a system in the past to a system in the future. It is shown that finite-time Lyapunov exponents calculated along a locally pullback attractive solution…

We identify a new universality class of phase transitions that arises in non-normal systems, challenging the classical view that transitions require eigenvalue instabilities. In traditional bifurcation theory, critical phenomena emerge when…

We explore the critical properties of the recently discovered finite-time dynamical phase transition in the non-equilibrium relaxation of Ising magnets after a temperature quench. The transition is characterized by a sudden switch in the…

In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…

Critical learning periods are periods early in development where temporary sensory deficits can have a permanent effect on behavior and learned representations. Despite the radical differences between biological and artificial networks,…

There is a ongoing debate whether generic early warning signals for critical transitions exist that can be applied across diverse systems. The human epileptic brain is often considered as a prototypical system, given the devastating and, at…

We consider a dissipative version of the standard nontwist map. Nontwist systems present a robust transport barrier, called the shearless curve, that becomes the shearless attractor when dissipation is introduced. This attractor can be…

The dynamics of a bouncing ball model under the influence of dissipation is investigated by using a two dimensional nonlinear mapping. When high dissipation is considered, the dynamics evolves to different attractors. The evolution of the…

Model studies indicate that many climate subsystems, especially ecosystems, may be vulnerable to 'tipping': a 'catastrophic process' in which a system, driven by gradually changing external factors, abruptly transitions (or 'collapses')…

In this work, we study the unpredictability of seasonal infectious diseases considering a SEIRS model with seasonal forcing. To investigate the dynamical behaviour, we compute bifurcation diagrams type hysteresis and their respective…

The synchronization of coupled chaotic systems represents a fundamental example of self organization and collective behavior. This well-studied phenomenon is classically characterized in terms of macroscopic parameters, such as Lyapunov…

We investigate the emergence of universal dynamical scaling in quantum critical spin systems adiabatically driven out of equilibrium, with emphasis on quench dynamics which involves non-isolated critical points (i.e., critical regions) and…

In complex systems, external parameters often determine the phase in which the system operates, i.e., its macroscopic behavior. For nearly a century, statistical physics has extensively studied systems' transitions across phases,…