Recently, a new classification of nonlinear dynamics has been introduced by Leonov and Kuznetsov, in which two kinds of attractors are concentrated, i.e. self-excited and hidden ones. Self-excited attractor has a basin of attraction excited from unstable equilibria. So, from that point of view, most known systems, like Lorenz’s system, Rössler’s system, Chen’s system, or Sprott’s system, belong to

Recently, a new classification of nonlinear dynamics has been introduced by Leonov and Kuznetsov, in which two kinds of attractors are concentrated, i.e. self-excited and hidden ones. Self-excited attractor has a basin of attraction excited from unstable equilibria. So, from that point of view, most known systems, like Lorenz's system, Rössler's system, Chen's system, or Sprott's system, belong to

This paper introduces new meta-heuristic optimization algorithms for extracting the parameters of the Cole-impedance model. It is one of the most important models providing best fitting with the measured data. The proposed algorithms inspired by nature are known as Flower Pollination Algorithm (FPA) and Moth-Flame Optimizer (MFO). The algorithms are tested over sets of both simulated and

This paper presents a generalization of Soliman's four-phase oscillator into the fractional-order domain. The extra degrees of freedom provided by the fractional-order parameters α and β add more flexibility to the design of the circuit. The design procedure and equations of the proposed oscillator are presented and verified using Matlab and PSPICE. Also, the stability analysis for fractional

This paper proposes a hardware platform implementation on FPGA for two fractional-order derivative operators. The Grünwald-Letnikov and Caputo definitions are realized for different fractional orders. The realization is based on non-uniform segmentation algorithm with a variable lookup table. A generic implementation for Grünwald-Letnikov is proposed and a 32 bit Fixed Point Booth multiplier radix

In this chapter, new control schemes to achieve inverse generalized synchronization (IGS) between fractional order chaotic (hyperchaotic) systems with different dimensions are presented. Specifically, given a fractional master system with dimension n and a fractional slave system with dimension m, the proposed approach enables each master system state to be synchronized with a functional

In this chapter, new control schemes to achieve inverse generalized synchronization (IGS) between fractional order chaotic (hyperchaotic) systems with different dimensions are presented. Specifically, given a fractional master system with dimension n and a fractional slave system with dimension m, the proposed approach enables each master system state to be synchronized with a functional

This paper is an extension of V-shape multi-scroll butterfly attractor in the fractional-order domain. The system complexity is increased by the new dynamics introduced by the fractional operator which make it more suitable for random signal generator. The effect of system parameters on controlling the attractor shape is investigated and compared with the integer order attractor. Maximum Lyapunov

This paper discusses the FPGA implementation of the fractional-order derivative as well as two fractional-order chaotic systems where one of them has controllable multi-scroll attractors. The complete hardware architecture of the Grünwald-Letnikov (GL) differ-integral is realized with different memory window sizes. As an application of the proposed circuit, a complete fractional-order FPGA

Pinched hysteresis is considered to be a signature of the existence of memristive behavior. However, this is not completely accurate. In this chapter, we are discussing a general equation taking into consideration all possible cases to model all known elements including memristor. Based on this equation, it is found that an opposite behavior to the memristor can exist in a nonlinear inductor or a