Strange—Nonchaotic—Attractor—Like Behaviors in Coupled Map SYstems

In a coupled map system,an attractor which seems to be strange nonchaotic attractor(SNA)is discovered for nonzero measure in parameter range,The attractor has nonpositive Lyapunov exponent(LE) and discrete structure.We call it strange-nonchaotic-attractor-like(SNA-like) behavior because the size of its size of its discrete structure decreases with the computing precision increasing and the true SNA does not change.The SNA-like behavior in the autonomous system is born when the truncation error of round-off is amplified to the size of the discrete part of the attractor during the long time interval of positive local LE.The SNA-like behavior is easily mistaken for a true SNA judging merely from the largest LE and the phase portrait in double precision computing.In non-autonomous system an SNA-like attractor is also found.

Strange-Nonchaotic-Attractor-Like Behaviors in Coupled Map System

In a coupled map system, an attractor which seems to be strange nonchaoticattractor (SNA) is discovered for nonzero measure in parameter range. Theattractor has nonpositive Lyapunov exponent (LE) and discrete structure. Wecall it strange-nonchaotic-attractor-like (SNA-like) behavior because thesize of its discrete structure decreases with the computing precisionincreasing and the true SNA does not change. The SNA-like behavior in theautonomous system is born when the truncation error of round-off isamplified to the size of the discrete part of the attractor during the longtime interval of positive local LE. The SNA-like behavior is easily mistakenfor a true SNA judging merely from the largest LE and the phase portrait indouble precision computing. In non-autonomous system an SNA-like attractor is also found.