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Based on the Lu system, a new chaotic system is constructed, which can generate a Lorenz-like attractor, Chen-like attractor, Lu-like attractor and new attractor when its parameters are chosen appropriately. The detailed dynamical behaviours of this system are also investigated, including equilibria and stability, bifurcations, and Lyapunov exponent spectrum. Moreover, a novel analogue circuit diagram is designed for the verification of various attractors.

A meminductor is a new type of memory device. It is of importance to study meminductor model and its application in nonlinear circuit prospectively. For this purpose, we present a novel mathematical model of meminductor, which considers the effects of internal state variable and therefore will be more consistent with future actual meminductor device. By using several operational amplifiers, multipliers, capacitors and resistors, the equivalent circuit of the model is designed for exploring its characteristics. This equivalent circuit can be employed to design meminductor-based application circuits as a meminductor emulator. By employing simulation experiment, we investigate the characteristics of this meminductor driven by sinusoidal excitation. The characteristic curves of current-flux (i-φ), voltage-flux (v-φ), v-ρ (internal variable of meminductor) and φ-ρ for the meminductor model are given by theoretical analyses and simulations. The curve of current-flux (i-φ) is a pinched hysteretic loop passing through the origin. The area bounding each sub-loop deforms as the frequency varies, and with the increase of frequency, the shape of the pinched hysteretic loop tends to be a straight line, indicating a dependence on frequency for the meminductor. Based on the meminductor model, a meminductive Wien-bridge chaotic oscillator is designed and analyzed. Some dynamical properties, including equilibrium points and the stability, bifurcation and Lyapunov exponent of the oscillator, are investigated in detail by theoretical analyses and simulations. By utilizing Lyapunov spectrum, bifurcation diagram and dynamical map, it is found that the system has periodic, quasi-periodic and chaotic states. Furthermore, there exist some complicated nonlinear phenomena for the system, such as constant Lyapunov exponent spectrum and nonlinear amplitude modulation of chaotic signals. Moreover, we also find the nonlinear phenomena of coexisting bifurcation and coexisting attractors, including coexistence of two different chaotic attractors and coexistence of two different periodic attractors. The phenomenon shows that the state of this oscilator is highly sensitive to its initial valuse, not only for chaotic state but also for periodic state, which is called coexistent oscillation in this paper. The basic mechanism and potential applications of the existing attractors are illustrated, which can be used to generate robust pseudo random sequence, or multiplexed pseudo random sequence. Finally, by using the equivalent circuit of the proposed meminducive model, we realize an analog electronic circuit of the meminductive Wien-bridge chaotic system. The results of circuit experiment are displayed by the oscilloscope, which can verify the chaotic characteristics of the oscillator. The oscillator, as a pseudo random signal source, can be used to generate chaotic signals for the applications in chaotic cryptography and secret communications.

A memcapacitor is a new type of memory capacitor. Before the advent of practical memcapacitor, the prospective studies on its models and potential applications are of importance. For this purpose, we establish a mathematical memcapacitor model and a corresponding circuit model. As a potential application, based on the model, a memcapacitor oscillator is designed, with its basic dynamic characteristics analyzed theoretically and experimentally. Some circuit variables such as charge, flux, and integral of charge, which are difficult to measure, are observed and measured via simulations and experiments. Analysis results show that besides the typical period-doubling bifurcations and period-3 windows, sustained chaos with constant Lyapunov exponents occurs. Moreover, this oscillator also exhibits abrupt chaos and some novel bifurcations. In addition, based on the digital signal processing (DSP) technology, a scheme of digitally realizing this memcapacitor oscillator is provided. Then the statistical properties of the chaotic sequences generated from the oscillator are tested by using the test suit of the National Institute of Standards and Technology (NIST). The tested randomness definitely reaches the standards of NIST, and is better than that of the well-known Lorenz system.

A 3.125 GHz Clock Recovery (CR) circuit used in the 6.25Gbps SerDes for Backplane Communication Receiver is described. Bang-bang PLL architecture is utilized for its high operation speed. An Alexander phase detector (PD) and a LC voltage-control oscillator (VCO) are involved in the circuit. The behavior of the nonlinear bang-bang PLL is modeled to give approximate evaluation of the loop stability. The circuit has been implemented in a standard 0.18 μm CMOS technology. The test result indicates that the frequency of the VCO is from 3 GHz to 3.35 GHz, the voltage gain is 270 MHz/V, and the phase noise is −118.38 dBc/Hz @1 MHz. The chip consumes less than 81 mW with 1.8 V power supply, and occupies 0.5 mm2 area.

In terms of analysis of permanent magnet synchronous motor (PMSM)drive system, the CARIMA (controlled auto-regressive integrated moving average) model of the object and the predicted PI velocity controller which was based on generalized predictive control (GPC) was established, the parameters of the model were identified by RLSM (recursive least squares method).

To develop real world memristor application circuits, an equivalent circuit model which imitates memductance (memory conductance) of the HP memristor is presented. The equivalent circuit can be used for breadboard experiments for various application circuit designs of memristor. Based on memductance of the realistic HP memristor and Chua’s circuit a new chaotic oscillator is designed. Some basic dynamical behaviors of the oscillator, including equilibrium set, Lyapunov exponent spectrum, and bifurcations with various circuit parameters are investigated theoretically and numerically. To confirm the correction of the proposed oscillator an analog circuit is designed using the proposed equivalent circuit model of an HP memristor, and the circuit simulations and the experimental results are given.

A meminductor is a new type of nonlinear inductor with memory, which is generalized from the concept of a memristor and defined by current-flux. This paper presents a flux-controlled meminductor model with a smooth quadratic function and designs its corresponding equivalent circuit, which can be used as an emulator to imitate the behavior of a meminductor when actual solid-state meminductor has not yet appeared. Furthermore, a new chaotic oscillator is designed based on this meminductor model, and the dynamical behaviors of the oscillator are investigated, such as chaotic attractors, equilibrium points, Lyapunov exponent spectrum, bifurcations and dynamical map of the system, etc. Bifurcation analysis shows that the meminductor can make the oscillator produce periodic and chaotic oscillations. Moreover, an analog circuit is designed to confirm the correction of the proposed oscillator using the proposed equivalent circuit model of meminductor. It is shown that the experimental results are in good agreement with that of the numerical simulations and the theoretical analysis.

The dependence of sensitivity on initial conditions is the essence of chaos. And the randomness of chaos originates from the high sensitivity to initial values, which is measured by the Lyapunov exponents. It is found in this paper that the cascade of chaotic systems can considerably improve the Lyapunov exponents of cascade chaos and other dynamic properties. Therefore, in this paper, we study the cascade of chaotic systems and the influence on dynamic performances of the cascade chaos, and we present the definition and conditions of chaotic system cascade. It is proved in theory that the Lyapunov exponent of cascade chaos system is a sum of Lyapunov exponents of cascade subsystems. Appropriate cascade for chaotic systems can increase system parameters and expand parameter regions of chaos mapping and full mapping, thereby enhancing initial condition sensitivity of chaotic map and security of chaotic pseudo-random sequences. For logistic map, cubic map and tent map, the dynamic characteristics of logistic-logistic, logistic-cubic and logistic-tent cascade are investigated in detail, verifying the improvements on dynamic characteristics of cascade chaos systems. The proposed chaotic cascade system can be used to generate better pseudo-random sequences for initial condition sensitivity and security.