Chaotic Circuit based on Memristive Elements

A novel memristive elements-based chaotic circuit only containing three elements of memristor, memcapacitor and meminductor is highlighted in this paper. The state equations of the memristive circuit are described, and the dynamical behaviors such as equilibrium set, Lyapunov exponents and bifurcation diagram are revealed by theoretical analyses and numerical simulations. Simulation results demonstrate that the sum of five Lyapunov exponents in this circuit is negative and the maximal Lyapunov exponent is equal to 0.1773, which verifies typical characteristics of limit cycle and 1-scroll chaotic attractor. The most striking feature is that this system to build a high-dimensional dynamic equation only using three circuit elements and exhibit rich phenomenon of period and chaotic behavior. Moreover, equivalent realization circuit are design to verify the theoretical analyses and numerical simulations.