Double crises in two-parameter forced oscillators by generalized cell mapping digraph method

By means of generalized cell mapping digraph method, a crisis of sinusoidally forced oscillators is observed as a system parameter is varied. The crisis happens when a chaotic attractor collides with a regular saddle or a chaotic saddle, and is called a regular crisis or a chaotic crisis, respectively. By increasing a small constant bias in the forcing and considering both the system parameter and bias together as controls, a double crisis vertex in a two-parameter plane is determined, at which four curves of crises meet and four distinct crises coincide. The two patterns of such a double crisis vertex are investigated, namely, two regular boundary crises compounded with two chaotic interior crises and two chaotic boundary crises compounded with two chaotic interior crises.