Damage spreading in the one-dimensional Hinrichsen-Domany model

Arashiro, Everaldo; Felício, J. R. Drugowich de

doi:10.1590/s0103-97332000000400007

Cited by 2 publications

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“…To analyse the relation between the spatial distribution of species and persistence and to find the thresholds of coexistence we carry out numerical simulations. A particularly useful numerical method for models with absorbing states, is the so-called time-dependent simulation (or spreading analysis) [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. This method allows us to obtain the phase boundaries together with the critical exponents.…”

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confidence: 99%

The threshold of coexistence and critical behaviour of a predator–prey cellular automaton

Arashiro

Tomé

2007

J. Phys. A: Math. Theor.

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We study a probabilistic cellular automaton to describe two population biology problems: the threshold of species coexistence in a predator-prey system and the spreading of an epidemic in a population. By carrying out time-dependent simulations we obtain the dynamic critical exponents and the phase boundaries (thresholds) related to the transition between an active state, where prey and predators present a stable coexistence, and a prey absorbing state. The estimates for the critical exponents show that the transition belongs to the directed percolation universality class. In the limit where the cellular automaton maps into a model for the spreading of an epidemic with immunization we observe a crossover from directed percolation class to the dynamic percolation class. Patterns of growing clusters related to species coexistence and spreading of epidemic are shown and discussed.

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Section: Introductionmentioning

confidence: 99%

The threshold of coexistence and critical behaviour of a predator–prey cellular automaton

Arashiro

Tomé

2007

J. Phys. A: Math. Theor.

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Stochastic dynamics of coupled systems and damage spreading

et al. 2003

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We study the damage spreading in the one-dimensional Ising model by means of the stochastic dynamics resulting from coupling the system and its replica by a family of algorithms that interpolate between the heat bath and the Hinrichsen-Domany algorithms. At high temperatures the dynamics is exactly mapped to the DomanyKinzel probabilistic cellular automaton. Using a mean-field approximation and Monte Carlo simulations we find the critical line that separates the phase where the damage spreads from the one where it does not.

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Damage spreading in the one-dimensional Hinrichsen-Domany model

Cited by 2 publications

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The threshold of coexistence and critical behaviour of a predator–prey cellular automaton

The threshold of coexistence and critical behaviour of a predator–prey cellular automaton

Stochastic dynamics of coupled systems and damage spreading

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