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

A hyperjerk system described by a single fourth-order ordinary differential equation of the form [Formula: see text] has been referred to as a snap system. A damping-tunable snap system, capable of an adjustable attractor dimension ([Formula: see text]) ranging from dissipative hyperchaos ([Formula: see text]) to conservative chaos ([Formula: see text]), 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 [Formula: see text] , 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).