Related papers: Entropy of random chaotic interval map with noise …
We consider effect of stochastic sources upon self-organization process being initiated with creation of the limit cycle induced by the Hopf bifurcation. General relations obtained are applied to the stochastic Lorenz system to show that…
Quantum chaotic maps can efficiently generate pseudo-random states carrying almost maximal multipartite entanglement, as characterized by the probability distribution of bipartite entanglement between all possible bipartitions of the…
The nature of coarse graining is intuitively "obvious", but it is rather difficult to find explicit and calculable models of the coarse graining process (and the resulting entropy flow) discussed in the literature. What we would like to…
If the state space of a homogeneous continuous-time Markov chain is too large, making inferences - here limited to determining marginal or limit expectations - becomes computationally infeasible. Fortunately, the state space of such a chain…
We consider a discrete time hidden Markov model where the signal is a stationary Markov chain. When conditioned on the observations, the signal is a Markov chain in a random environment under the conditional measure. It is shown that this…
The Fluctuation Relation for a stationary state, kept at constant energy by a deterministic thermostat - the Gallavotti-Cohen Theorem -- relies on the ergodic properties of the system considered. We show that when perturbed by an…
We consider endomorphisms of a compact manifold which are expanding except for a finite number of points and prove the existence and uniqueness of a physical measure and its stochastical stability. We also characterize the zero-noise limit…
We explore the properties of discrete-time stochastic processes with a bounded state space, whose deterministic limit is given by a map of the unit interval. We find that, in the mesoscopic description of the system, the large jumps between…
Estimating the entropy based on data is one of the prototypical problems in distribution property testing and estimation. For estimating the Shannon entropy of a distribution on $S$ elements with independent samples, [Paninski2004] showed…
We develop a formalism to describe the discrete-time dynamics of systems containing an arbitrary number of interacting species. The individual-based model, which forms our starting point, is described by a Markov chain, which in the limit…
We demonstrate deterministic extensive chaos in the dynamics of large sparse networks of theta neurons in the balanced state. The analysis is based on numerically exact calculations of the full spectrum of Lyapunov exponents, the entropy…
When chaotic signals are used in practical communication systems, it is essential to control and eventually limit the spectral bandwidth occupied by these signals. One way to achieve this goal is to insert a discrete-time filter into a…
The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…
A detailed study of the mean-field solution of Langevin equations with multiplicative noise is presented. Three different regimes depending on noise-intensity (weak, intermediate, and strong-noise) are identified by performing a…
Numerical experiments recently discussed in the literature show that identical nonlinear chaotic systems linked by a common noise term (or signal) may synchronize after a finite time. We study the process of synchronization as function of…
Consider tossing a collection of coins, each fair or biased towards heads, and take the distribution of the total number of heads that result. It is natural to conjecture that this distribution should be 'more random' when each coin is…
We study countably monotone and Markov interval maps. We establish sufficient conditions for uniqueness of a conjugate map of constant slope. We explain how global window perturbation can be used to generate a large class of maps satisfying…
Two-dimensional mappings obtained by coupling two piecewise increasing expanding maps are considered. Their dynamics is described when the coupling parameter increases in the expanding domain. By introducing a coding and by analysing an…
Chaotic synchronization is generally extremely sensitive to the presence of noise and other inference in the channel. Is this sensitivity a fundamental property of chaotic synchronization or is it related to the choice of synchronization…
Chaos thresholds of the $z$-logistic maps $x_{t+1}=1-a|x_t|^z$ $(z>1; t=0,1,2,...)$ are numerically analysed at accumulation points of cycles 2, 3 and 5. We verify that the nonextensive $q$-generalization of a Pesin-like identity is…