Related papers: Multistability in dynamical systems
Let f be a diffeomorphism of a compact finite dimensional boundaryless manifold M exhibiting infinitely many coexisting attractors. Assume that each attractor supports a stochastically stable probability measure and that the union of the…
We identify the mechanism behind the existence of intensity induced chimera states in globally coupled oscillators. We find that the effect of intensity in the system is to cause multistability by increasing the number of fixed points. This…
We study dynamical systems composed of a set of linearly coupled quadratic maps which, if uncoupled, would be on the Feigenbaum accumulation point. For two units we prove the existence of an infinite number of sinks for an open set of…
Research in multistable systems is a flourishing field with countless examples and applications across scientific disciplines. I present a catalog of multistable dynamical systems covering relevant fields of knowledge. This work is focused…
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…
We present a dynamical system that naturally exhibits two unstable attractors that are completely enclosed by each others basin volume. This counter-intuitive phenomenon occurs in networks of pulse-coupled oscillators with delayed…
Multistability cannot be derived from any theoretical model that is based on a monostable master equation. On the other hand, multistability is experimentally-observed in a variety of quantum systems. A master equation having a nonlinear…
We report the first experimental observation of extreme multistability in a controlled laboratory investigation. Extreme multistability arises when infinitely many attractors coexist for the same set of system parameters. The behavior was…
For low-dimensional chaotic attractors there is usually a single number of unstable dimensions for all of its periodic orbits and we can say such attractors exhibit "mono-chaos". In high-dimensional chaotic attractors, trajectories are…
Concepts like `typicality' and the `eigenstate thermalization hypothesis' aim at explaining the apparent equilibration of quantum systems, possibly after a very long time. However, these concepts are not concerned with the specific way in…
In this paper, we will show that a periodic nonlinear, time-varying dissipative system that is defined on a genus-p surface contains one or more invariant sets which act as attractors. Moreover, we shall generalize a result in [Martins,…
Multistability -- the emergence of multiple stable states under identical conditions -- is a hallmark of nonlinear complexity and an enabling mechanism for multilevel optical memory and photonic computing. Its realization in a compact…
Optomechanical systems are known to exhibit a rich set of complex dynamical features including various types of chaotic behavior and multi-stability. Although this exotic behavior has attracted an intense research interest, the utilization…
Throughout the literature on Neural Cellular Automata (NCAs), it is often taken for granted that the systems learn attractors. This is shown through evolving the system for many timesteps and noting visual similarity to the goal state.…
We study dynamics and bifurcations of 2-dimensional reversible maps having a symmetric saddle fixed point with an asymmetric pair of nontransversal homoclinic orbits (a symmetric nontransversal homoclinic figure-8). We consider…
Steering of attractors in multistable systems is used to increase the available parameter domains which lead to stable dynamics in nonlinear physical systems, reducing substantially undesirable effects of parametric inaccuracy and noise.…
The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates…
We propose a methodology to analyze synchronization in an ensemble of diffusively coupled multistable systems. First, we study how two bidirectionally coupled multistable oscillators synchronize and demonstrate the high complexity of the…
Continuous attractors offer a unique class of solutions for storing continuous-valued variables in recurrent system states for indefinitely long time intervals. Unfortunately, continuous attractors suffer from severe structural instability…
We consider dynamical systems given by interval maps with a finite number of turning points (including critical points, discontinuities) possibly of different critical orders from two sides. If such a map $f$ is continuous and piecewise…