Hyperchaos and horseshoe in a 4D memristive system with a line of equilibria and its implementation

We study a four‐dimensional system modified from a three‐dimensional chaotic circuit by adding a memristor, which is a new fundamental electronic element with promising applications. Although the system has a line of infinitely many equilibria, our studies show that when the strength of the memristor increases, it can exhibit rich interesting dynamics, such as hyperchaos, long period‐1 orbits, transient hyperchaos, as well as non‐attractive behaviors frequently interrupting hyperchaos. To verify the existence of hyperchaos and reveal its mechanism, a horseshoe with two‐directional expansion is studied rigorously in detail by the virtue of the topological horseshoe theory and the computer‐assisted approach of a Poincaré map. At last, the system is implemented with an electronic circuit for experimental verification.