The chaotic characteristics of two dimensional random coupled logistic map are studied in this paper. The coupling coefficients of the system are considered to obey two points distribution，and the phase diagram and Lyapunov exponents are exploited to judge the system state. Numerical results show that, the system can lead to chaos based on periodic bifurcation and Hopf bifurcation when the coupling coefficients jump between the chaotic and non-chaotic regions according to certain probability. In particular, the probability density functions of the system orbits reveal the evolution of the system.
