Heteroclinic Orbits Seized from CAPUTO Fractional-Order Lorenz System with Memristor

By constructing two distinct Lyapunov-like functions and employing concepts of α-/ω-limit sets, this article reinvestigates the Caputo fractional-order (0<α≤1) memristor-based Lorenz system, and rigorously proves that there exists a pair of heteroclinic orbits. The analytical findings are validated via numerical simulations, and as far as we know, these results have not been previously reported, thereby extending the relevant research outcomes in this field.