Nonlinear Computation

Abstract

Nonlinear Computation will provide a framework for the computational science and engineering of the future. Topics such as bifurcation and chaos, and methods such as continuation and branch switching, and features such as stability and sensitivity are basic ingredients in the attempt to understand our world. Nonlinear Computation is indispensable when we try to predict and simulate the dynamics of states in the biological systems we consist of, in the ecological and economical systems we live in, and in the technical systems we make use of. This paper essentially consists of three parts. The first part (Sec. 1) explains what nonlinear computation means. The second part (Secs. 2–5) presents a survey on nonlinear phenomena, and on the methods of nonlinear computation. The final part (Secs. 6 and 7) will speculate on visions and trends for the next decades.