A Damping-Tunable Snap System: From Dissipative Hyperchaos to Conservative Chaos

Abstract

A hyperjerk system described by a single fourth-order ordinary differential equation of the form x⃜=f(x⃛,x¨,x˙,x) has been referred to as a snap system. A damping-tunable snap system, capable of an adjustable attractor dimension (DL) ranging from dissipative hyperchaos (DL4) to conservative chaos (DL=4), is presented for the first time, in particular not only in a snap system, but also in a four-dimensional (4D) system. Such an attractor dimension is adjustable by nonlinear damping of a relatively simple quadratic function of the form Ax2, easily tunable by a single parameter A. The proposed snap system is practically implemented and verified by the reconfigurable circuits of field programmable analog arrays (FPAAs).

Keywords

• adjustable attractor dimension
• conservative chaos
• dissipative hyperchaos
• FPAA
• hyperjerk
• tunable damping