Critical Exponent of Chaotic Transients in Nonlinear Dynamical Systems

The average lifetime of a chaotic transient versus a system parameter is studied for the case wherein a chaotic attractor is converted into a chaotic transient upon collision with its basin boundary (a crisis). Typically the average lifetime T depends upon the system parameter p via T~|p-pc|^-γ, where pc denotes the value of p at the crisis and we call γ the critical exponent of the chaotic transient. A theory determining γ for two-dimensional maps is developed and compared with numerical experiments. The theory also applies to critical behavior at interior crises.