New family of 4-D hyperchaotic and chaotic systems with quadric surfaces of equilibria

This paper reports 4-D hyperchaotic and chaotic systems with various quadric surfaces of equilibria. A known and systematic search procedure is used to generate the proposed systems. Six cases have non-degenerate quadric surfaces (ellipsoid, spheroid, sphere, elliptic hyperboloid of one sheet, circular hyperboloid of one sheet) type of equilibria and two cases have degenerate quadric surfaces (elliptic cylinder, circular cylinder) type of equilibria. All the cases in the new systems have coexistence of chaotic attractors. Chaotic natures of the new systems are confirmed by using various numerical tools. MATLAB simulation results are further validated by circuit implementations.