Publication

Markov chain modeling of chaotic wandering in simple coupled chaotic circuits

Martin Hasler
2001
Conference Papers

Abstract

In this study, chaotic wandering phenomenon observed in simple coupled chaotic circuits is modeled by Markov chains. As coupling parameter increases, the solution of the coupled chaotic circuits starts to wander chaotically over 6 different phase states which are stable for smaller value of the parameter. The wandering is modeled by a first order and sedond order Markov chains with the 6 states plus 3 intermediate states. Stationary probability function, expected sojourn time and probability density of sojourn time are calculated from transition probabilities. These statistical properties are compared with those obtained from computer simulations

Official source

https://infoscience.epfl.ch/entities/publication/60429749-5558-4f03-bdff-000f374dd468

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Martin Hasler
2001
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/60429749-5558-4f03-bdff-000f374dd468

About this result

Related concepts (32)

Markov chain

A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairs now." A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC).

Markov model

In probability theory, a Markov model is a stochastic model used to model pseudo-randomly changing systems. It is assumed that future states depend only on the current state, not on the events that occurred before it (that is, it assumes the Markov property). Generally, this assumption enables reasoning and computation with the model that would otherwise be intractable. For this reason, in the fields of predictive modelling and probabilistic forecasting, it is desirable for a given model to exhibit the Markov property.

Markov chain Monte Carlo

In statistics, Markov chain Monte Carlo (MCMC) methods comprise a class of algorithms for sampling from a probability distribution. By constructing a Markov chain that has the desired distribution as its equilibrium distribution, one can obtain a sample of the desired distribution by recording states from the chain. The more steps that are included, the more closely the distribution of the sample matches the actual desired distribution. Various algorithms exist for constructing chains, including the Metropolis–Hastings algorithm.

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Markov chain modeling of chaotic wandering in simple coupled chaotic circuits

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