Page 222 - Artificial Intelligence in the Age of Neural Networks and Brain Computing

4. Multistability in Physics and Biology 213

state as the dynamics evolves [34,44]. As described by the complementarity
principle, such switching between metastable states is the result of spontaneous
symmetry breaking in self-organizing dynamical systems [38].
Coupled map lattices (CML) give a convenient mathematical model of meta-
stable behaviors. In CMLs, the dynamics of each part of the system is described
by some nonlinear mapping function, while the parts are connected according to
lattice geometry. Examples of a CML over a 1-dimensional lattice (circle) with
periodic boundary condition are shown in Fig. 10.5. Various types of coupling
are considered, including local, mesoscopic,and global coupling, respectively
[45]. In the case of local coupling, a node interacts only with its direct neighbors
on the lattice, which means two neighbors (left and right) over the 1D lattice. The
other extreme case is global or mean field coupling, when each node interacts with

FIGURE 10.5
Multistability effects due to mesoscopic/intermediate-range interactions. Example of
coupled map lattices with local, intermediate, and global (mean field) interactions. The
emergence of low-dimensional attractor structures is demonstrated for mesoscopic
coupling. The phase diagram with regions of high synchrony and low synchrony identifies
chimera states with coexisting nonsynchronous and coherent states based on laser
studies.
Based on R. Kozma, Intermediate-range coupling generates low-dimensional attractors deeply in the chaotic
region of one-dimensional lattices, Physics Letters A 244 (1e3) (1998) 85e91.