We propose a novel floating memristor chaotic circuit with serial connection between a charge-controlled memristor and an inductor.Basic dynamic properties of the system are investigated with conventional dynamic analysis method. It shows that the system produces a pair of "heart" type attractors about origin symmetry. Simulation results indicate that strange attractors like bow tie type are observed as voltage and electricity signal in observing chaotic attractors are generalized to power and energy signal. Hopf bifurcation behavior is analyzed and verified by numerical simulation. It shows that the system can produce two bifurcation behaviors by adjusting parameters. They are Hopf bifurcation and anti-period doubling bifurcation. Remarkable feature of the citcuit is that it adopts a floating memristor, and with different initial state it generates nonlinear phenomena including coexisting chaotic and coexisting chaotic-periodic attractors.

Compared with active piecewise linear(PWL) and cubic smooth memristor model adopted in most memristor-based chaotic circuits, charge-control quadratic memristor model is more practical, which is derived from a passive device fabricated by HP Labs. Based on the model and a topological dual structure of Chua's chaotic circuit, a memristor-based fourth-order chaotic circuit was designed. As is verified by theoretical analysis, simulation and circuit realizations, the charge-control quadratic memristor-based chaotic circuit has complex dynamical behaviors relying on initial state of memristor. Meanwhile, non-linear dynamical phenomenon of state transition is generated along with variation of initial state, time and system parameters. An eye of scroll and an eye of limit cycle are observed in phase diagrams of chaotic circuits

A simplest cascade memristor chaotic circuit is constructed with a charge-controlled memristor,an inductance,a capacitance and a negative conductance. Dynamic properties of the circuit are demonstrated by means of equilibrium stability,Lyapunov exponent spectra and bifurcation diagrams. Numerical simulation shows that a class of particular single scroll chaotic attractors is produced in the case of one equilibrium point. With increase of system parameter,the circuit exhibits complicated chaotic behaviors. Pspice simulations are well consistent with theoretical analysis and numerical simulation.

We study a three-dimensional quadratic autonomous chaotic system.Basic dynamic characteristics are analyzed via theoretical analysis and numerical simulation.Lyapunov exponent spectrum,Lyapunov dimension as well as bifurcation diagram are calculated.An electronic circuit is designed to realize the chaotic system.Relationships between system parameters and circuit parameters are built.The circuit is simulated using Pspice.Simulation results confirm the analysis.The system discussed is different from Lorenz system,Rössler system,Chen system and Lü system.The chaotic circuit is simple and practical.