New Trends in Nonlinear Dynamics by Walter Lacarbonara & Balakumar Balachandran & Jun Ma & J. A. Tenreiro Machado & Gabor Stepan

Author:Walter Lacarbonara & Balakumar Balachandran & Jun Ma & J. A. Tenreiro Machado & Gabor Stepan
Language: eng
Format: epub
ISBN: 9783030347246
Publisher: Springer International Publishing

With D getting greater, the whole time duration of rectangular spiral wave formation grows very fast. But there exists a critical value of D cr at which transition of patterns occurs. It is reasonable to assume that when the parameter D gets approach to critical value D cr, the time duration of pattern formation tends to infinity. If power law of time duration and absolute value |D − D cr| holds, the phenomenon called critical slowing down is discovered.

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where λ > 0 is the critical slowing down index. We plot the time duration and absolute of |D − D cr| in double logarithmic coordinates in Fig. 4b. The blue line is the fitted curve whose slope gives exact value of the critical slowing down index λ. In our simulation λ is 0.92. And the critical value of D cr is about 3.172 by carefully checking. As a matter of fact, the phenomenon of critical slowing down exists in both sides of the critical value of D cr. Similarly, λ of D > D cr is determined as 0.91, which is close to that of D < D cr.

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