Complex dynamics and initial state effects in a two-dimensional sine-bounded memristive map

Abstract

Recently, discrete memristor maps can be directly constructed using discrete memristors. However, some discrete memristors with reciprocal polynomial memristances cannot be directly used to generate mapping models. To achieve an available memristive map, a simple and effective implementation scheme is proposed to construct a two-dimensional (2-D) sine-bounded memristive map (SBMM). The proposed map has line invariant point and its stability is extremely related to parameters and memristor initial state. The parameter-dependent complex dynamics, coexisting attractors with riddled attraction basin, and initial state-induced dynamics effect are disclosed using several numerical measures. SBMM has complex dynamics distributions with initial state effects and can generate chaotic and hyperchaotic attractors with riddled attraction basins. These chaotic/hyperchaotic sequences have excellent performance and can be applied to generate pseudorandom binary number generators (PBNGs). Besides, FPGA hardware implementation is performed, and the numerical results are verified by experiments.