Coupled Map Lattice - Visual Phenomena

Visual Phenomena

The unique qualitative classes listed above can be visualized. By applying the Kaneko 1983 model to the logistic map, several of the CML qualitative classes may be observed. These are demonstrated below, note the unique parameters:

Frozen Chaos Pattern Selection Chaotic Brownian Motion of Defect
Figure 1: Sites are divided into non-uniform clusters, where the divided patterns are regarded as attractors. Sensitivity to initial conditions exist relative to a < 1.5. Figure 2: Near uniform sized clusters (a = 1.71, ε = 0.4). Figure 3: Deflects exist in the system and fluctuate chaotically akin to Brownian motion (a = 1.85, ε = 0.1).
Defect Turbulence Spatiotemporal Intermittency I Spatiotemporal Intermittency II
Figure 4: Many defects are generated and turbulently collide (a = 1.895, ε = 0.1). Figure 5: Each site transits between a coherent state and chaotic state intermittently (a = 1.75, ε = 0.6), Phase I. Figure 6: The coherent state, Phase II.
Fully Developed Spatiotemporal Chaos Traveling Wave
Figure 7: Most sites independently oscillate chaotically (a = 2.00, ε = 0.3). Figure 8: The wave of clusters travels at 'low' speeds (a = 1.47, ε = 0.5).

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