Special section on bifurcations

Abstract

The term “bifurcation” means changes in qualitative structure of dynamical systems due to a small change of the parameter values. In the engineering systems such as communication, circuits and control systems, the bifurcation relates deeply to border of stability and generation of complicated nonlinear phenomena including chaos. There exist various kinds of bifurcation phenomena. Classification and recognition of the phenomena are very important to understand the nonlinear dynamics and to develop their efficient applications. This special section consists of two invited papers and ten regular papers. They have valuable contents which are important to grasp the state-of-the-art of the study and to trigger further development of the study. The first invited paper (Tsumoto, Ueta, Yoshinaga and Kawakami) discusses fundamental theory and computation methods of bifurcation analysis in nonlinear dynamical systems. The second invited paper (In, Kho, Longhini and Palacios) discusses global bifurcation of coupled overdamped bistable systems with applications to sensor devices. The ten regular papers discuss a variety of topics: a visualization method for chaotic attractors in planer discrete systems, numerical sensitivity in the analysis of a high-dimensional oscillator, bifurcation of a piecewise linear 1D map of a simple hybrid dynamical system, analysis of super-stable periodic orbits of 1D map with a trapping window, bifurcation of an interrupted dynamical system with a periodic threshold, bifurcation scenarios of inhibitory responses in a simple spiking neuron model, dependence of parameters on chaos-based solvers of combinatorial optimization problems, the particle swarm optimization algorithm for designing the class-E amplifier, basic analysis of digital spike maps and a cellular array system for parallel generation of pseudo-random binary sequences. On behalf of the editorial board, this guest editor expresses his sincere thanks to all the authors for their excellent contributions. He also thanks the reviewers and the members of the editorial board, especially, Assoc. prof. Hiroyuki Torikai of Osaka University and Assoc. prof. Takuji Kosaka of Oita University for their supports on publishing this special section. It may be some destiny that this special section is published on the 100th anniversary of the death of Henri Poincaré who introduced the term “bifurcation” in 1885.