Related papers: On multistability behavior of Unstable Dissipative…
Let $\mathcal{F}$ be a $C^2$ random partially hyperbolic dynamical system. For the unstable foliation, the corresponding unstable metric entropy, unstable topological entropy and unstable pressure via the dynamics of $\mathcal{F}$ on the…
This paper concerns the adaptive control problem for a class of nonlinear stochastic systems in which the state update is given by a nonlinear function of linear dynamics plus additive stochastic noise. Such systems arise in a wide range of…
Scroll waves are three-dimensional analogs of spiral waves. The linear stability spectrum of untwisted and twisted scroll waves is computed for a two-variable reaction-diffusion model of an excitable medium. Different bands of modes are…
Large assemblies of nonlinear dynamical units driven by a long-wave fluctuating external field are found to generate strong turbulence with scaling properties. This type of turbulence is so robust that it persists over a finite parameter…
We study the transport properties of passive inertial particles in a $2-d$ incompressible flows. Here the particle dynamics is represented by the $4-d$ dissipative embedding map of $2-d$ area-preserving standard map which models the…
A dynamical phase transition from reversible to irreversible behavior occurs when particle suspensions are subjected to uniform oscillatory shear, even in the Stokes flow limit. We consider a more general situation with non-uniform strain…
A system far from equilibrium is characterized by unconventional many-body dynamical effects, which can lead to anomalous density fluctuations and mass transport. Interestingly, these structural and dynamic features often emerge…
The wake of a body moving across the isopycnals of a strongly stratified fluid is characterized by the presence of an intense jet which, under certain circumstances, may become unstable. To get insight into the phenomenology of this…
Consider a dynamical system given by a planar differential equation, which exhibits an unstable periodic orbit surrounding a stable periodic orbit. It is known that under random perturbations, the distribution of locations where the…
In classical mechanics, solutions can be classified according to their stability. Each of them is part of the possible trajectories of the system. However, the signatures of unstable solutions are hard to observe in an experiment, and most…
The phenomenon of slow passage through a Hopf bifurcation is ubiquitous in multiple-timescale dynamical systems, where a slowly-varying quantity replacing a static parameter induces the solutions of the resulting slow-fast system to feel…
We consider the motion of a particle subjected to the constant gravitational field and scattered inelasticaly by hard boundaries which possess the shape of parabola, wedge, and hyperbola. The billiard itself performs oscillations. The…
In laboratory studies and numerical simulations, we observe clear signatures of unstable time-periodic solutions in a moderately turbulent quasi-two-dimensional flow. We validate the dynamical relevance of such solutions by demonstrating…
Network theory is rapidly changing our understanding of complex systems, but the relevance of topological features for the dynamic behavior of metabolic networks, food webs, production systems, information networks, or cascade failures of…
We investigate the hopping dynamics between different attractors in a multistable system under the influence of noise. Using symbolic dynamics we find a sudden increase of dynamical entropies, when a system parameter is varied. This effect…
This paper investigates the different behaviors of the process equation and parameters of their occurrences. The process equation is a multistable one dimensional map with nonlinear feedback and can show various behaviors such as period…
Here we numerically study a model of excitable media, namely, a network with occasionally quiet nodes and connection weights that vary with activity on a short-time scale. Even in the absence of stimuli, this exhibits unstable dynamics,…
We show that a collection of independent Ising spins evolving stochastically can display surprisingly large fluctuations towards ordered behaviour, as quantified by certain types of time-integrated plaquette observables, despite the…
The prospect of a system possessing two or more stable states for a given excitation condition is of topical interest with applications in information processing networks. In this work, we establish the remote transfer of bistability from a…
The dynamics of two nonlinear Bloch systems is studied from the viewpoint of bifur- cation and a particular parameter space has been explored for the stability analysis based on stability criterion. This enables the choice of the desired…