ANALYSIS OF PERIODIC ORBITS IN COUPLED DIGITAL RETURN MAPS

Abstract

This paper considers periodic orbits in coupled digital spike maps. The digital spike map is a digital dynamical system defined by a set of points. The digital spike map can generate a variety of periodic orbits. Digital dynamical systems are suitable for precise numerical analysis, hardware implementation using FPGA and can be applied to various systems including neural networks. We can obtain the coupled digital spike map by mutual coupling of two digital spike maps. The coupled system can exhibit a variety of periodic orbits. First, we introduce typical examples generated by coupled digital spike maps. Next, we introduce two simple feature quantities for quantitative analysis of the behavior of periodic orbits. The first quantity evaluates complexity of periodic orbits. The second quantity evaluates stability of periodic orbits. We construct feature planes using two feature quantities for analysis. We focus on maximum periodic orbits because the phenomena are complex