A Novel Lorenz-like Attractor and Stability and Equilibrium Analysis

This paper introduces a novel 3D periodically forced extended Lorenz-like system and illustrates a single thick two-scroll attractor with potential unboundedness whose time series of the second state variable present some certain random characteristics rather than pure periodicity yielded by that system itself. Combining the Lyapunov function and the definitions of both the α-limit set and ω-limit set, the following rigorous results are proved: infinitely many heteroclinic orbits to two families of parallel parabolic-type non-hyperbolic equilibria, two families of infinitely many pairs of isolated equilibria, an infinite set of isolated equilibria, and infinitely many pairs of isolated equilibria.