^{1}

^{2}

^{3}

^{1}

^{2}

^{3}

A new memristive system is presented in this paper. The peculiarity of the model is that it does not display any equilibria and exhibits periodic, chaotic, and also hyperchaotic dynamics in a particular range of the parameters space. The behavior of the proposed system is investigated through numerical simulations, such as phase portraits, Lyapunov exponents, and Poincaré sections, and circuital implementation confirmed the hyperchaotic dynamic.

Since the first hyperchaotic attractor introduced by Rössler [

After the realization of a solid-state thin film two-terminal memristor at Hewlett-Packard Labs [

Motivated by complex dynamical behaviors of hyperchaotic systems, noticeable characteristics of memristor, and unknown features of hidden attractors, a novel memristor-based hyperchaotic system without equilibrium is proposed in this paper. The paper is organized as follows. In the next section, the model of memristive device is introduced. This memristive device is used as the main component in the new memristive system, which is proposed in Section

Chua and Kang [

Hysteresis loops of the proposed memristive device (

Based on the introduced memristive device (

When

When

Hyperchaotic attractor without equilibrium obtained from system (

Poincaré map in the

It is well known that Lyapunov exponents measure the exponential rates of the divergence and convergence of nearby trajectories in the phase space of the chaotic system [

Lyapunov exponents of system (

Bifurcation diagram of

Implementation of chaotic/hyperchaotic systems by using electronic circuits provides an effective approach for discovering dynamics of such system. This physical approach can avoid the uncertainties arising from systematic and statistical errors in numerical simulations [

Therefore, in this section, a circuital realization of system (

Circuital schematic of the new hyperchaotic system without equilibrium (

Circuitry realization which emulates the memristive device (

The designed circuit is implemented in the electronic simulation package OrCAD (see Figure

OrCAD schematic of the new hyperchaotic system without equilibrium (

Hyperchaotic attractor of the designed electronic circuit obtained from OrCAD (a) in the

The existence of a memristor-based chaotic system without equilibrium has been studied in this paper. Although four-dimensional memristive systems often only generate chaos, the presence of a memristive device leads the proposed system to a hyperchaotic system with hidden attractors. The system has a rich dynamical behavior as confirmed by the examples of attractors reported and by the numerical Poincaré map presented. Because there is little knowledge about the special features of such system, future works will continue focusing on dynamical behaviours as well as the possibility of control and synchronization of such system.

Despite the fact that equations (

The authors declare that there is no conflict of interests regarding the publication of this paper.

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant no. 102.99-2013.06.