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.
Grebogi, C., Ott, E., & Yorke, J. A. (1986). Critical Exponent of Chaotic Transients in Nonlinear Dynamical Systems. Physical Review Letters, 57(11), 1284-1287. https://doi.org/10.1103/PhysRevLett.57.1284