Search results for "Continuous parameter"

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From deterministic cellular automata to coupled map lattices

2016

A general mathematical method is presented for the systematic construction of coupled map lattices (CMLs) out of deterministic cellular automata (CAs). The entire CA rule space is addressed by means of a universal map for CAs that we have recently derived and that is not dependent on any freely adjustable parameters. The CMLs thus constructed are termed real-valued deterministic cellular automata (RDCA) and encompass all deterministic CAs in rule space in the asymptotic limit $\kappa \to 0$ of a continuous parameter $\kappa$. Thus, RDCAs generalize CAs in such a way that they constitute CMLs when $\kappa$ is finite and nonvanishing. In the limit $\kappa \to \infty$ all RDCAs are shown to ex…

Statistics and ProbabilityGeneral Physics and AstronomyFOS: Physical sciencesPattern Formation and Solitons (nlin.PS)Space (mathematics)01 natural sciences010305 fluids & plasmasLinear stability analysis0103 physical sciencesLimit (mathematics)Statistical physics010306 general physicsMathematical PhysicsBifurcationPhysicsCellular Automata and Lattice Gases (nlin.CG)Quiescent stateStatistical and Nonlinear PhysicsNonlinear Sciences - Chaotic DynamicsNonlinear Sciences - Pattern Formation and SolitonsCellular automatonNonlinear Sciences - Adaptation and Self-Organizing SystemsHomogeneousModeling and SimulationContinuous parameterChaotic Dynamics (nlin.CD)Adaptation and Self-Organizing Systems (nlin.AO)Nonlinear Sciences - Cellular Automata and Lattice Gases
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