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This study aims to predict the unstable period-1 orbit (UPO-1) of DC–DC converters and find analytical expressions to describe it.

Nonlinear dynamical phenomena of a peak–current–mode controlled direct current–direct current (DC–DC) Boost converter are discussed briefly first. Then fast fourier transform (FFT) analysis of state variables under different dynamic states is provided, and the characteristic of the harmonic content in different states is summarized. Following these, a scientific hypothesis on the harmonic content of the UPO-1 is presented, and the Equivalent Small Parameter method is adopted then, thus analytic-form expressions of the UPO-1 can be derived.

According to results of theoretical analysis, numerical simulations and experiments, this paper illustrates that, like stable period-1 orbit, the UPO-1 is also made up of the DC component and harmonics with integer times of switching frequency.

This work provides an unreported approach for extracting the UPO-1 of DC–DC converters, which is mainly based on predicting the harmonic structure information of the orbit. According to experimental parts of the work, it shows that the stabilizer can be designed easier by using the proposed method. Additionally, from a broader perspective, the results could also have implications in a wide class of forced oscillation systems.

Due to the coupling between the direct-axis current, quadrature-axis current and rotor speed, the dynamic response could be strongly nonlinear. Besides, if the working condition is severe, the loading is no longer constant and multiple harmonics could be introduced. In this paper, the periodic motions for brushless motor will be solved, and accurate analytic solution will be obtained through the proposed method. The purpose of this study is to provide accurate analytic solution of periodic motions for brushless motor with fluctuated loading, which is a dynamic system with strong nonlinearity.

A newly developed semi-analytic algorithm called discrete implicit maps is used to give analytic solutions for both stable and unstable motions for such a motor.

The accurate analytic expressions for stable and unstable periodic motions have been obtained. For unstable motion, it can stay on the unstable orbit for many periods without any controller. Through bifurcation analysis, the parameter sensitivity has been obtained which can be a suggestion for design and operation.

This paper provides all possible analytical solutions for period-1 motion as well as the unstable motions in a range of system parameters. It offers a chance to control the unstable motion for such a motor.

Cascaded DC-DC converters system is the main structure of distributed power system, and it has complex nonlinear phenomena during operation, which affect the power quality. Therefore, the dynamic behavior of the cascaded buck converter and boost converter system, as one of the typical cascaded DC-DC converters systems is analyzed.

Firstly, the studied cascaded system of the buck converter with peak current control and the boost converter with PI current control is introduced and its discrete modeling is built. Then, the Jacobian matrix of the cascaded system is calculated to research the stability when the parameter change. Finally, simulation by PSIM and experiments are carried out to verify the theoretical analysis.

The coexistence of fast and slow time scale bifurcations with the changes of reference current and input voltage are studied in the cascaded system, and using simulation analysis to further study the sensitivity of the inductor current of the front-stage converter and back-stage converter to different parameters.

A discrete model of the cascaded buck converter and boost converter system is established, and its dynamic behavior is analyzed in detail for the first time.

Computer simulations were done extensively in order to study non‐linear dynamics of laser‐plasma interaction in InSb semiconductor. We constructed the modified Duffing kind of non‐linear semiconductor plasma oscillator equation. Collision frequency is found to be dominant parameter to influence the bifurcation, chaos, hysteresis and bistable effects of plasma wave. Small windows of higher period cascade above the critical value of laser parameter (α₁α₂) in the chaos region are observed. Laser‐plasma exhibits too much chaotic regime at lower value of laser driving frequency (δ). Hysteresis and bistable regions of plasma wave are presented and the conditions for their occurence are identified. The unstable regions completely merge at higher value of effective collision frequency (γ).

In the design and development stage of the power converter systems, an abnormal intermittency is naturally experienced in nonautonomous system because of coupling of the interference signals. The study of identifying the possible conditions at which such an undesirable operation emerges is vital. Hence, the purpose of this paper is to explore the intermittent instabilities that evolve in the voltage-mode controlled quadratic buck converter when the sinusoidal interference signal coupled in reference voltage.

Voltage-mode controlled quadratic buck converter with the sinusoidal interference signal coupled in reference voltage manifests a symmetrical period-doubling bifurcation in intermittent periods for significant interference signal strength with the frequency near to the switching frequency or its rational multiples. The complete dynamics of the system is investigated for the various inference signal frequencies by numerical simulations.

Here, the intermittent instabilities are verified using a simple Filippov’s method with supporting evidence of Floquet multipliers (eigenvalues) movement. The analytical result obtained is found to agree well with the simulation results.

Power supplies are liable to an ambiguous complex behavior when it is seldom protected against the interference signal. The experimental study has made an attempt to explicit a detailed behavior observed in voltage-mode controlled quadratic buck converter when a sinusoidal intruding signal of different amplitude and frequency are coupled with the reference voltage. Such an analysis gives considerable focus for the power electronics engineers to meet the design requirements.

To the authors’ knowledge, all the research works on intermittent instabilities in power converters are analyzed only using conventional method of Poincare map technique which emerges to be complicated when the order of the system is higher. Alternatively, in this paper, Filippov’s technique is used for stability analysis of periodic orbit. The evolution of bifurcation point is predicted by the calculating the Floquet multipliers of monodromy matrix, and it is known to achieve the same objective as the Poincare map technique in much more straightforward way.

The purpose of this paper is to construct a proportion-integral-type (PI-type) memristor, which is different from that of the previous memristor emulator, but the constructing memristive chaotic circuit possesses line equilibrium, leading to the emergence of the initial conditions-related dynamical behaviors.

This paper presents a PI-type memristor emulator-based canonical Chua’s chaotic circuit. With the established mathematical model, the stability region for the line equilibrium is derived, which mainly consists of stable and unstable regions, leading to the emergence of bi-stability because of the appearance of a memristor. Initial conditions-related dynamical behaviors are investigated by some numerically simulated methods, such as phase plane orbit, bifurcation diagram, Lyapunov exponent spectrum, basin of the attraction and 0-1 test. Additionally, PSIM circuit simulations are executed and the seized results validate complex dynamical behaviors in the proposed memristive circuit.

The system exhibits the bi-stability phenomenon and demonstrates complex initial conditions-related bifurcation behaviors with the variation of system parameters, which leads to the occurrence of the hyperchaos, chaos, quasi-periodic and period behaviors in the proposed circuit.

These memristor emulators are simple and easy to physically fabricate, which have been increasingly used for experimentally demonstrating some interesting and striking dynamical behaviors in the memristor-based circuits and systems.

This paper aims to classify the inductorless Chua’s circuits into two types from the topological structures and construct a chaotic circuit under this new classification framework.

In this paper, two types of inductorless Chua’s circuit models are presented from topological structure, among which the first type of inductorless Chua’s circuit (FTICC) model is much closer to the original Chua’s circuit. Under this classification framework, a new inductorless Chua’s circuit that belongs to the FTICC model is built by replacing LC parallel resonance of the original Chua’s circuit with a second order Sallen–Key band pass filter.

Compared with a paradigm of a reported inductorless Chua’s circuit that belongs to the second type of inductorless Chua’s circuit (STICC) model, the newly proposed circuit can present the attractors which are much more closely to the original Chua’s attractors. The dynamical behaviors of coexisting period-doubling bifurcation patterns and boundary crisis are discovered in the newly proposed circuit from both numerical simulations and experimental measurements. Moreover, a crisis scenario is observed that unmixed pairs of symmetric coexisting limit cycles with period-3 traverse through the entire parameter interval between coexisting single-scroll chaotic attractors and double-scroll chaotic attractor.

The newly constructed circuit enriches the family of inductorless Chua’s circuits, and its simple topology with small printed circuit board size facilitates the various types of engineering applications based on chaos.