BOPS Bogdanov Map Gaussian mixture model Hopf bifurcation Hubbard tree Lyapunov exponents Non-equilibrium four-dimensional chaotic system PRNG S-Box algorithm Thurston’s algorithm adaptive approximator-based control approximate entropy chaos chaotic flow chaotic map chaotic maps chaotic system chaotic systems circuit design coexistence complex systems complex-variable chaotic system core entropy electronic circuit realization empirical mode decomposition entropy entropy analysis entropy measure existence external rays