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 Kaneko¹,
• The Rulkov Map²

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