Open AccessDynamical properties of discontinuous and noninvertible two-dimensional map
Author(s) -
Jun Dai,
Chu Xiang-Sheng,
Daihai He
Publication year - 2006
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.55.3979
Subject(s) - attractor , dissipative system , piecewise , cusp (singularity) , impossibility , bounded function , fractal , trajectory , dynamical systems theory , chaotic , computer science , statistical physics , mathematics , physics , mathematical analysis , geometry , artificial intelligence , quantum mechanics , political science , law
This paper reports five different features in piecewise continuous and noninvertible system described by two conservative maps or one conservative map and another dissipative map. The features are as follows: the stochastic web bounded by images of discontinuous borderline is the only chaotic trajectory; phase collapse is caused by the irreversibility which makes some points to have two pre-images; fat fractal forbidden web induced by irreversibility; riddled-like attraction basin in stochastic web and forbidden web, when there are different attractors coexisting; and the impossibility to tell to which attractor an initial condition will approach. In an integrate-and-fire circuit, we find that the features still exist in the circuit system described by two dissipative maps, so they are common features in discontinuous and noninvertible maps.