cmlattice 0.0.3

An implementation of coupled map lattices.

cmlattice

cmlattice provides a python implementation of various types of coupled map lattices. A coupled map lattice, or CML, is a dynamic system that models the behavior of nonlinear systems.

This package contains several different models, all of which can be broadly described as cmls:

• A standard CML with logistic state function,
• The CML model primarily studied by Kaneko[^1],
• The Rulkov Map[^2]

A Standard CML

# initialize the lattice object
lattice = CoupledMapLattice(n=10, r=4, mu=0, sigma=1)

# run a hundred step simulation
STEPS = 100
sim_gen = lattice.simulate(STEPS)

# unpack the generator
sim = list(sim_gen)

# finally, vizualize your simulation
viz = Visualization(lattice)
v = viz.animate()

A Kaneko Lattice

# initialize the lattice object
lattice = KanekoLattice(n=10, r=4, mu=0, sigma=1)

# run a hundred step simulation
STEPS = 100
sim_gen = lattice.simulate(STEPS)

# unpack the generator
sim = list(sim_gen)

# finally, vizualize your simulation
viz = Visualization(lattice)
v = viz

An Uncoupled Rulkov Lattice

# initialize the lattice object
lattice = RulkovLattice(n=10, r=4, mu=0, sigma=1, epsilon=1)

# run a hundred step simulation
STEPS = 100
sim_gen = lattice.simulate(STEPS)

# unpack the generator
sim = list(sim_gen)

# finally, vizualize your simulation
viz = Visualization(lattice)
v = viz

Chaos

These models are particularly useful in studying choatic, dynamic systems. For example, in one dimension choosing an r parameter of greater than 3.57 for a standard lattice will behave choatically.

Citations

[^1]: Kunihiko Kaneko, Period-Doubling of Kink-Antikink Patterns, Quasiperiodicity in Antiferro-Like Structures and Spatial Intermittency in Coupled Logistic Lattice: Towards a Prelude of a “Field Theory of Chaos”, Progress of Theoretical Physics, Volume 72, Issue 3, September 1984, Pages 480–486, https://doi.org/10.1143/PTP.72.480

[^2]: N.F. Rulkov (2001). "Regularization of Synchronized Chaotic Bursts". Physical Review Letters. 86 (1): 183–186. arXiv:nlin/0011028. Bibcode:2001PhRvL..86..183R. doi:10.1103/physrevlett.86.183. PMID 11136124. S2CID 7016788