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CLIMBING UP DYNAMICAL HIERARCHY

    https://doi.org/10.1142/9789814503372_0012Cited by:1 (Source: Crossref)
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    Abstract:

    A brief review on the climbing-up of dynamical hierarchy is presented, inspired by Otto Rössler’s philosophy. The hierarchy rises from chaos to hyperchaos, and then to (hyper)∞ chaos. (Hyper)∞ chaos is studied in coupled map lattices as a model for spatiotemporal chaos. A further step of hierarchy from (hyper)∞ chaos leads to the hierarchical dynamics, as is discussed in globally coupled maps. This hierarchical dynamics is suggested to be relevant to neural nets, the economics, and the evolution. As a next step of hierarchy, chaotic itinerancy is discussed in globally coupled maps. It leads to a dynamical system whose effective degrees of freedom changes with time. Possible relation of this dynamics with coherent structure in turbulence is discussed. As a further step of hierarchy, the evolutionary dynamical process is discussed. The dynamics of punctuated equlibrium may be related with chaotic itinerancy. However, other essentially novel dynamics is necessary to include the novelty pressure and genetic fusion. How high should we climb up the dynamical hierarchy to reach intelligence?.