Related papers: Crisis in time-dependent dynamical systems
Turbulence is a widely observed state of fluid flows, characterized by complex, nonlinear interactions between motions across a broad spectrum of length and time scales. While turbulence is ubiquitous, from teacups to planetary atmospheres,…
Two known distinct examples of one-dimensional systems which are known to exhibit a phase transition are critically examined: (A) a lattice model with harmonic nearest-neighbor elastic interactions and an on-site Morse potential, and (B)…
Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion…
In the present paper which is a sequel to [N.B. Volkov and A.M. Iskoldsky The dynamics of vortex structures and states of current: 1;[1]], the dynamics of non-equilibrium phase transitions and states of current in electrophysical systems…
Turbulence is one of the most frequently encountered non-equilibrium phenomena in nature yet characterising the transition that gives rise to it has remained an elusive task. Although in recent studies critical points marking the onset of…
Uncovering and understanding universal dynamics in matter far from equilibrium remains a key challenge. In this work, we identify a so far unrecognized form of universal behavior that emerges after a sudden symmetry-breaking quench at…
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…
Dynamical phase transitions are defined through non-analyticities of the survival probability of an out-of-equilibrium time-evolving state at certain critical times. They ensue from zeros of the corresponding survival amplitude. By…
Nonlinear dynamical systems subjected to a combination of noise and time-varying forcing can exhibit sudden changes, critical transitions or tipping points where large or rapid dynamic effects arise from changes in a parameter that are…
Some dynamical properties for a dissipative time-dependent oval-shaped billiard are studied. The system is described in terms of a four-dimensional nonlinear mapping. Dissipation is introduced via inelastic collisions of the particle with…
We have numerically studied the trapping problem in a two-dimensional lattice where particles are continuously generated. We have introduced interaction between particles and directionality of their movement. This model presents a critical…
Globally coupled populations of phase rotators with linear adaptive coupling can exhibit collective bursting oscillations between asynchronous and partially synchronized states, which can be either periodic or chaotic. Here, we analyze the…
We present a numerical study of a two-lane version of the stochastic non-equilibrium model known as the totally asymmetric simple exclusion process. For such a system with open boundaries, and suitably chosen values of externally-imposed…
Non-autonomous dynamical systems help us to understand the implications of real systems which are in contact with their environment as it actually occurs in nature. Here, we focus on systems where a parameter changes with time at small but…
The structural properties of an economical model for a confined plasma turbulence governor are investigated through bifurcation and stability analyses. A close relationship is demonstrated between the underlying bifurcation framework of the…
Bifurcations can cause dynamical systems with slowly varying parameters to transition to far-away attractors. The terms ``critical transition'' or ``tipping point'' have been used to describe this situation. Critical transitions have been…
Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful conceptual and mathematical tools were…
We consider an infinite network of globally-coupled phase oscillators in which the natural frequencies of the oscillators are drawn from a symmetric bimodal distribution. We demonstrate that macroscopic chaos can occur in this system when…
Recently, a model of opinion formation with kinetic exchanges has been proposed in which a spontaneous symmetry breaking transition was reported [M. Lallouache et al, Phys. Rev. E, {\bf 82} 056112 (2010)]. We generalise the model to…
Dynamical phase transitions can occur in isolated quantum systems that are brought out of equilibrium by sudden parameter changes. We discuss the characterization of such dynamical phase transitions based on the statistics of produced…