Related papers: Chaotic singular maps
Chaotic functions are characterized by sensitivity to initial conditions, transitivity, and regularity. Providing new functions with such properties is a real challenge. This work shows that one can associate with any Boolean network a…
The sequences, given by a 7D map have been analysed by means of the methods, widely used to detect chaos in the real world in order to test their sensitivity to chaotic features of a non-linear system determined by comparatively high number…
We consider dynamics of a scalar piecewise linear "saw map" with infinitely many linear segments. In particular, such maps are generated as a Poincar\'e map of simple two-dimensional discrete time piecewise linear systems involving a…
We uncover and characterize different chaotic transport scenarios on perfect periodic surfaces by controlling the chaotic dynamics of particles subjected to periodic external forces in the absence of a ratchet effect. After identifying…
In the sciences in general, the phrase "route to chaos" has come to refer to a metaphor when some physical, biological, economic, or social system transitions from one exhibiting order to one displaying randomness (or chaos). Sometimes the…
Self-adjusting, or adaptive systems have gathered much recent interest. We present a model for self-adjusting systems which treats the control parameters of the system as slowly varying, rather than constant. The dynamics of these…
We improve previous results by exhibiting a construction that contains all known examples. A suficient condition for the existence of robustly transitive maps displaying singularities on a certain large class of compact manifolds is given.
Chaotic dynamics is always characterized by swarms of unstable trajectories, unpredictable individually, and thus generally studied statistically. It is often the case that such phase-space densities relax exponentially fast to a limiting…
In a generic dynamical system chaos and regular motion coexist side by side, in different parts of the phase space. The border between these, where trajectories are neither unstable nor stable but of marginal stability, manifests itself…
We give a definition of chaos for a continuous self-map of a general topological space. This definition coincides with the Devanney definition for chaos when the topological space happens to be a metric space. We show that in a uniform…
We analyze a one-dimensional piecewise continuous discrete model proposed originally in studies on population ecology. The map is composed of a linear part and a power-law decreasing piece, and has three parameters. The system presents both…
We treat $n$-dimensional piecewise-linear continuous maps with two pieces, each of which has exactly one unstable direction, and identify an explicit set of sufficient conditions for the existence of a chaotic attractor. The conditions…
A type of chaos called laminar chaos was found in singularly perturbed dynamical systems with periodically [Phys. Rev. Lett. 120, 084102 (2018)] and quasiperiodically [Phys. Rev. E 107, 014205 (2023)] time-varying delay. Compared to…
We investigate the spatio-temporal dynamics of coupled chaotic systems with nonlocal interactions, where each element is coupled to its nearest neighbors within a finite range. Depending upon the coupling strength and coupling radius, we…
Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…
Metastability is a physical phenomenon ubiquitous in first order phase transitions. A fruitful mathematical way to approach this phenomenon is the study of rare transitions Markov chains. For Metropolis chains associated with Statistical…
General hierarchical lattices of coupled maps are considered as dynamical systems. These models may describe many processes occurring in heterogeneous media with tree-like structures. The transition to turbulence via spatiotemporal…
We propose a stochastic sampling approach to identify stability boundaries in general dynamical systems. The global landscape of Lyapunov exponent in multi-dimensional parameter space provides transition boundaries for stable/unstable…
Chaotic dynamics is widely used to design pseudo-random number generators and for other applications such as secure communications and encryption. This paper aims to study the dynamics of discrete-time chaotic maps in the digital (i.e.,…
On timescales that greatly exceed an orbital period, typical planetary orbits evolve in a stochastic yet stable fashion. On even longer timescales, however, planetary orbits can spontaneously transition from bounded to unbound chaotic…