Abstract
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.
Highlights
Since the first hyperchaotic attractor introduced by Rossler [1], hyperchaotic systems have been intensively studied due to their potential applications in many fields of interest
After the realization of a solid-state thin film twoterminal memristor at Hewlett-Packard Labs [7], a considerable number of potential memristor-based applications have been reported like high-speed low-power processors [8], adaptive filter [9], pattern recognition systems [10], associative memory [11], neural networks [12, 13], programmable analog integrated circuits [14], and so on [15, 16]
This hyperchaotic system can be considered as a dynamical system with hidden attractor [24, 25] because it is impossible to verify the chaotic attractor by choosing an arbitrary initial condition in the vicinity of the unstable equilibria [23]
Summary
Since the first hyperchaotic attractor introduced by Rossler [1], hyperchaotic systems have been intensively studied due to their potential applications in many fields of interest. The intrinsic nonlinear characteristic of memristor has been exploited in implementing novel chaotic oscillators with complex dynamics [17, 18]. In [21], starting from a memristorbased canonical Chua’s circuit, a five-dimensional hyperchaotic oscillator was introduced, while a four-dimensional hyperchaotic memristive system with a line equilibrium was reported by Li et al [22]. The last example belongs to a new category of chaotic systems with hidden attractors. Motivated by complex dynamical behaviors of hyperchaotic systems, noticeable characteristics of memristor, and unknown features of hidden attractors, a novel memristorbased hyperchaotic system without equilibrium is proposed in this paper.
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