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The memristor has received significant attention recently. The memristor is a potential candidate for various applications like switching devices, low-power sensors, neural networks, bio-inspired implementations, memory elements, programmable logic, signal processing, and so on. It is worth noting that researchers have attempted to evaluate the impact of the memristor for fast computation like artificial intelligence chips. In this chapter, we would like to summarize briefly recent researches related to memristor, mem-systems, and their neuromorphic applications. Especially, neuromorphic circuits and artificial intelligence applications are addressed. In addition, challenges, current issues and future trends are discussed.

This chapter puts forward the analysis of a novel memristor-based four dimensional (4D) chaotic system without equilibria and its projective synchronization using nonlinear active control technique. The proposed memristor-based novel 4D chaotic system has total nine terms with two nonlinear terms. Different qualitative and quantitative tools: time series, phase plane, Lyapunov exponents, bifurcation diagram, Lyapunov dimension, Poincare map are used to analyze the proposed memristor-based system. The proposed system has periodic, 2-torus quasi-periodic, chaotic, and chaotic 2-torus attractors, which are confirmed with the calculation of the system's Lyapunov exponents and bifurcation diagram. The proposed chaotic system has thumb and parachute shapes of Poincare map and satisfy unique and interesting behaviors. Such a memristor-based dissipative chaotic system is not available in the literature. Furthermore, the projective synchronization between memristor-based novel chaotic systems is achieved. The nonlinear active control laws are designed by using the sum of relevant variables of the systems and required global asymptotic stability condition is derived to achieve synchronization. Results are simulated in MATLAB environment and reflect that objectives are achieved successfully.

The memristor, a two-terminal electrical component, was invented by Chua and was considered as the fourth fundamental circuit element besides resistor, capacitor, and inductor. After the implementation of a solid-state memristor in HP laboratories, there are numerous researches related to memristor-based system. Theoretical models, fundamental features, numerical simulation and complexity of the memristor have been presented. Different kinds of memristors have been proposed such as the titanium dioxide memristor, polymeric memristor, layered memristor, ferroelectric memristor, spintronic memristor, and carbon nanotube memristor. It is worth noting that the memristor is a potential candidate for applications like switching devices, neural networks, and especially memory elements. Resistive random-access memory (RRAM or ReRAM) displays significant benefits for portable devices because of its non-volatile characteristic and small structure. In this work, we introduce an organic RRAM, which implemented by using commercial ink-jet printer. Design process and fabrication are described to show the advantages of our approaches. Moreover, a practical application example to demonstrate the feasibility of our RRAM is presented. We believe that the proposed RRAM is appropriate for emerging memories in smart devices.

In this chapter, the phenomenon of extreme multistability in a 4D hyperjerk memristive system is studied. The proposed system is a dynamical system with hidden attractors due to a line of equilibrium points. The behavior of the system is studied by using tools of nonlinear theory such as phase portrait, bifurcation diagram, and Lyapunov exponents.

This chapter investigates a novel three-dimensional chaotic system with an infinite number of equilibrium points, which are located on a parabola. Fundamental dynamical properties of the system are discovered through simulation tools of nonlinear theory such as phase portraits, Poincare map, Kaplan-Yorke dimension, Lyapunov exponents, and bifurcation diagram. In addition, an electronic circuit is designed and simulated by using the electronic simulation package OrCAD to demonstrate the feasibility of the proposed system. Adaptive control and adaptive synchronization of such a system with parabolic equilibrium are also reported.

Systems without equilibrium such as electromechanical models with rotation and electrical circuits with cylindrical phase space were studied a long time ago. However, chaotic systems without equilibrium have received significant attention recently after the introduction of hidden attractors. Interestingly, an attractor of a no-equilibrium system is hidden because its basin of attraction does not intersect with any neighborhood of an unstable fixed point. This chapter presents a 3D no-equilibrium system with hidden chaotic attractors. The fundamental qualitative properties of the proposed no-equilibrium system are discovered by using phase portraits, Poincare map, bifurcation diagram, and Lyapunov exponents. We have designed an electronic circuit to confirm the physical implementation of the theoretical no-equilibrium system. In addition, global chaos antisynchronization of the proposed system is investigated and confirmed by numerical simulations. Finally the fractional-order form of the proposed no-equilibrium chaotic system is studied in detail.

Conventional chaotic systems, such as the Lorenz system, Rossler system, Chen system, or Lu system, have a countable number of equilibrium points. Interestingly, a few unusual systems with infinite equilibria have been discovered recently. It is worth noting that from a computational point of view, that equilibria cannot support to identify the attractors in such systems. This chapter presents a three-dimensional chaotic system with an infinite number of equilibrium points. The fundamental properties of such a system are investigated by using equilibrium analysis, phase portraits, Poincare map, bifurcation diagram, and Lyapunov exponents. Interestingly, the system with infinite equilibria exhibits coexisting attractors. Chaos synchronization ability of the proposed system is studied via adaptive control. In addition, a fractional order form of the new system is also reported.