Dynamical behavior of a class of 4D memristive chaotic circuits was discussed, and attracting domain of multi-stability was studied. In order to guarantee efficiency and accuracy of calculation results, CPU+GPU large-scale computing power were introduced and more than 128 decimal places of precision GMP library and MPFR library were applied to calculate domain of corresponding attractor. Finally, existence of hyperchaos was proved by using method of topological horseshoe theory and constructing memristive analog circuit.

It is hard to apply topological horseshoe in 3D maps due to high dimension and complex structure since dimension of a chaotic attractor is often lower than its state space. We fit a surface with attractor near a selected unstable periodic orbit, and present a "dimension reduction" method to find topological horseshoes with one-directional expansion in 3D space. It is realized with a MATLAB toolbox. Compass walking model is shown to verify effectiveness, and illustrates detailed procedure for finding a topological horseshoe. It successfully verifys existence of chaotic gait and analyzes chaotic invariant set with horseshoe.