Related papers: Non-deterministic chaos
In this paper, we present a novel framework to synthesize robust strategies for discrete-time nonlinear systems with random disturbances that are unknown, against temporal logic specifications. The proposed framework is data-driven and…
We have investigated the "weak chaos" exponent to see if it can be considered as a classification parameter of different sandpile models. Simulation results show that "weak chaos" exponent may be one of the characteristic exponents of the…
Evolutionary game theory has traditionally employed deterministic models to describe population dynamics. These models, due to their inherent nonlinearities, can exhibit deterministic chaos, where population fluctuations follow complex,…
We examine the conjecture that entropy production in subsystems of a given system can be used as a dynamical criterion for quantum chaos in the latter. Numerical results are presented for finite dimensional spin systems as also for the…
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…
We predict that continuously monitored quantum dynamics can be chaotic. The optimal paths between past and future boundary conditions can diverge exponentially in time when there is time-dependent evolution and continuous weak monitoring.…
In experiments, the dynamical behavior of systems is reflected in time series. Due to the finiteness of the observational data set it is not possible to reconstruct the invariant measure up to arbitrary fine resolution and arbitrary high…
Classical chaos is marked by an extreme sensitivity to initial conditions, where infinitesimally close trajectories separate exponentially over time. In quantum mechanics, however, unitary evolution and the uncertainty principle preclude…
In this paper we consider the question of distributional chaos on non-compact metric dynamical systems. We focus on a shift space over a countable alphabet, the Baire Space. We prove that on the Baire Space subshifts of finite type exhibit…
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…
Here we define natural chaotic systems, like the earths weather and climate system, as chaotic systems which are open to the world so have constantly changing boundary conditions, and measurements of their states are subject to errors. In…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…
The paper deals with the theoretical analysis of a logistic system composed of at least two elements with distributed parameters. It has been shown that such a system may generate specific oscillations in spite of the fact that the…
A classical dynamical system can be viewed as a probability space equipped with a measure-preserving time evolution map, admitting a purely algebraic formulation in terms of the algebra of bounded functions on the phase space. Similarly, a…
Some physical processes, including the intensity fluctuations of a chaotic laser, the detection of single photons, and the Brownian motion of a microscopic particle in a fluid are unpredictable, at least on long timescales. This…
A stochastic model predictive control (SMPC) approach is presented for discrete-time linear systems with arbitrary time-invariant probabilistic uncertainties and additive Gaussian process noise. Closed-loop stability of the SMPC approach is…
It is shown that a paradigm of classical statistical mechanics --- the thermalization of a Brownian particle --- has a low-dimensional, deterministic analogue: when a heavy, slow system is coupled to fast deterministic chaos, the resultant…
Random walks serve as important tools for studying complex network structures, yet their dynamics in cases where transition probabilities are not static remain under explored and poorly understood. Here we study nonlinear random walks that…
The cloud of cold atoms obtained from a magneto-optical trap is known to exhibit two types of instabilities in the regime of high atomic densities: stochastic instabilities and deterministic instabilities. In the present paper, the…