This paper introduces an intensive discussion for the dynamical model of the love triangle in both integer and fractional-order domains. Three different types of nonlinearities soft, hard, and mixed between soft and hard, are used in this study. MATLAB numerical simulations for the different three categories are presented. Also, a discussion for how the kind of personalities affects the behavior of chaotic attractors is introduced. This paper suggests some explanations for the complex love relationships depending on the impact of memory (IoM) principle. Lyapunov exponents, Kaplan-Yorke

A generalized inverse memristor emulator is proposed based on two BJT transistors as a diode connected with a first order parallel RC filter. The mathematical model of the circuit is presented where the pinched hysteresis loops (PHLs) with different periodic stimuli are analyzed. The numerical, P-Spice simulations and experimental results are presented indicating that the introduced emulator is a simple voltage-controlled generalized inverse memristor. The results show that the PHLs area is increased with increasing the applied frequency. In addition, the proposed emulator is employed in a

In this paper, X-controlled universal fractional-order memelements (FOMEs) emulator is proposed. The emulation circuit is realized using second-generation current conveyor (CCII) and analog voltage multiplier (AVM)/divider block with two switches to control the type of memelements and emulator mode. The effect of the fractional-order capacitor (FOC) on the pinched hysteresis loop (HL) area and the range of frequency is discussed at different fractional-order α. Additionally, the higher-order meminductor, memristor, memcapacitor, and inverse memristor are discussed presenting multiple pinched

This paper proposes a new fractional-order multi-scrolls chaotic system. More complex systems and flexible ranges of the chaotic behavior are obtained due to the extra parameters added by the fractional-order. The proposed system has novel complex chaotic behaviors. The effect of changing the system parameters on the system behavior is investigated and their bifurcation diagrams have been provided. The MLE for the proposed system in integer and fractional domain has been discussed. It shows that the proposed chaotic system is richer in the case of fractional-order. A novel FPGA design

This paper proposes a generalized topology of a fractional-order inverse filter (FOF) using operational transresistance amplifiers (OTRA) block. Seven different configurations are extracted from the introduced topology employing generalized admittances. The generalized admittances increase the flexibility to provide different types of FOFs such as inverse fractional high pass filter (FHPF), inverse fractional low pass filter (FLPF), inverse fractional bandpass filter (FBPF), and inverse fractional notch filter (FNF). Numerical and PSPICE simulation results are presented for selected cases to

In this paper, three novel fractional-order CFOA-based inverse filters are introduced. The inverse low-pass, high-pass and band-pass responses are investigated using different approximation techniques. The studied approximations for the fractional-order Laplacian operator are the continued fraction expansion and Matsuda approximations. A comparison is held between the ideal filter characteristic and the realized ones from each approximation. A comparative study is summarized between the proposed circuits with some of the released inverse filters introduced in the literature. Foster-I

This paper proposes voltage- and current-controlled universal memelements emulators. They are employed to realize the floating and grounded fractional-order memelements. The proposed emulators are implemented using different active blocks such as the second-generation current conveyor (CCII), Differential input double output transconductance amplifier (DOTA + ), balanced output CCII, and Differential voltage current conveyor (DVCC) with analog voltage multiplier. One of the main characteristics of the memristive elements is hysteresis loop behaviour with one pinched point, and the higher-order

This paper introduces a study for the effect of using different floating-point representations on the chaotic system's behaviour. Also, it offers a comparison between the attractors at three different orders, (integer, fractional, and mixed-order). This comparison shows the minimum number of bits needed for all parameters to simulate the chaotic attractor in each case. Numerical simulations using Matlab are presented for all discussed chaotic systems. This study opens the door to implement chaotic systems and different applications digitally with low hardware area. The FPGA hardware

The mathematical formulae of six topologies of fractional-order Colpitts oscillator are introduced in this paper. Half of these topologies are based on MOS transistor, and the other half is based on BJT transistor. The design procedure for all of these topologies is proposed and summarized for each one. Stability analysis is very crucial in oscillators’ design, as oscillators should have its poles on the imaginary axis to obtain a sustained oscillation. Hence, determining the factors that control the oscillator’s stability is very important. An intensive study of the stability of Colpitts

In this paper, a generalized floating emulator block is proposed using grounded elements. The proposed emulator is a universal emulator that is used to realize any floating elements such as fractional-order element (FOE) and fractional-order memelements (FOME). Different implementations for the introduced emulator are presented using different active blocks and generalized impedances. The fractional-order parameters add an extra degree of controllability on the hysteresis loop (HL) and the location of the pinched point, which will be investigated. Circuit simulations for the proposed circuits