Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 12, Issue 4, Pages 827-834Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127402004772
Keywords
fractals; ordinary differential equations; stochastically switching inputs; electronic circuit
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We have proposed a process of generating fractals not from the results of chaotic dynamics, but from the switching of ordinary differential equations. This paper experimentally and numerically analyzes the dynamics of an electronic circuit driven by stochastically switching inputs. The following two results are obtained. First, the dynamics is characterized by a set Gamma(C) of trajectories in the cylindrical phase space, where C is a set of initial states on the Poincare section. Gamma(C) and C are attractive and unique invariant fractal sets that satisfy specific equations. The second result is that the correlation dimension of C is in inverse proportion to the interval of the switching inputs. These two findings move beyond the conventional theory based on contraction maps. It should be noted that the set C is constructed by noncontraction maps.
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