Open AccessRelaxation bursting and the mechanism of four-dimensional Chua's circuit with multiple interfaces
Author(s) -
Xiaofang Zhang,
Xiaoke Chen,
Bi Qin-Sheng
Publication year - 2013
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.62.010502
Subject(s) - bursting , attractor , chua's circuit , gravitational singularity , relaxation (psychology) , computer science , bifurcation , scale (ratio) , statistical physics , control theory (sociology) , physics , mathematical analysis , nonlinear system , mathematics , artificial intelligence , neuroscience , quantum mechanics , control (management) , biology
Based on the classical Chua's circuit, a four-dimensional Generalized Chua's circuit with multiple interfaces is established by introducing feedback elements. For the appropriate condition, there exists a difference in order of magnitude between the variables of state and a fast-slow coupled system, thereby forming a fast- and slow-coupled system at time scale. Analyzing the equilibrium points and the characteristics of the fast subsystems, and combining the theory of Clarke differential inclusions, the singularities on the non-smooth boundaries are explored. Two types of periodic bursting phenomena for different conditions are presented. Fast-slow analysis is employed to explore the special cluster phenomenon while the system trajectory passes across multiple interfaces. The coexisting different bursting mechanisms for the case with multiple attractors are explored in detail, while the influence of non-smooth bifurcations on bursting behavior is revealed.