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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.

This paper aims to investigate the singular Hopf bifurcation and mixed mode oscillations (MMOs) in the perturbed Bonhoeffer-van der Pol (BVP) circuit. There is a singular periodic orbit constructed by the switching between the stable focus and large amplitude relaxation cycles. Using a generalized fast/slow analysis, the authors show the generation mechanism of two distinct kinds of MMOs.

The parametric modulation can be used to generate complicated dynamics. The BVP circuit is constructed as an example for second-order differential equation with periodic perturbation. Then the authors draw the bifurcation parameter diagram in terms of a containing two attractive regions, i.e. the stable relaxation cycle and the stable focus. The transition mechanism and characteristic features are investigated intensively by one-fast/two-slow analysis combined with bifurcation theory.

Periodic perturbation can suppress nonlinear circuit dynamic to a singular periodic orbit. The combination of these small oscillations with the large amplitude oscillations that occur due to canard cycles yields such MMOs. The results connect the theory of the singular Hopf bifurcation enabling easier calculations of where the oscillations occur.

By treating the perturbation as the second slow variable, the authors obtain that the MMOs are due to the canards in a supercritical case or in a subcritical case. This study can reveal the transition mechanism for multi-time scale characteristics in perturbed circuit. The information gained from such results can be extended to periodically perturbed circuits.

In the inelastic stability analysis of plated structures, incremental‐iterative finite element methods sometimes encounter prohibitive solution difficulties in the vicinity of sharp limit points, branch points and other regions of abrupt non‐linearity. Presents an analysis system that attempts to trace the non‐linear response associated with these types of problems at minor computational cost. Proposes a semi‐heuristic method for automatic load incrementation, termed the adaptive arc‐length procedure. This procedure is capable of detecting abrupt non‐linearities and reducing the increment size prior to encountering iterative convergence difficulties. The adaptive arc‐length method is also capable of increasing the increment size rapidly in regions of near linear response. This strategy, combined with consistent linearization to obtain the updated tangent stiffness matrix in all iterative steps, and with the use of a “minimum residual displacement” constraint on the iterations, is found to be effective in avoiding solution difficulties in many types of severe non‐linear problems. However, additional procedures are necessary to negotiate branch points within the solution path, as well as to ameliorate convergence difficulties in certain situations. Presents a special algorithm, termed the bifurcation processor, which is effective for solving many of these types of problems. Discusses several example solutions to illustrate the performance of the resulting analysis system.

This paper aims to present bifurcation analysis of a magnetically supported coaxial rotor model in auxiliary bearings, which includes gyroscopic moments of disks and geometric coupling of the magnetic actuators.

Ten nonlinear equations of motion were solved using the Runge–Kutta method. The vibration responses were analyzed using dynamic trajectories, power spectra, Poincaré maps, bifurcation diagrams and the maximum Lyapunov exponent. The analysis was carried out for different system parameters, namely, the inner shaft stiffness, inter-rotor bearing stiffness, auxiliary bearing stiffness and disk position.

It was shown that dynamics of the system could be significantly affected by varying these parameters, so that the system responses displayed a rich variety of nonlinear dynamical phenomena, including quasi-periodicity, chaos and jump. Next, some threshold values were provided with regard to the design of appropriate parameters for this system. Therefore, the proposed work can provide an effective means of gaining insights into the nonlinear dynamics of coaxial rotor–active magnetic bearing systems with auxiliary bearings in the future.

This paper considered the influences of the inner shaft stiffness, inter-rotor bearing stiffness, auxiliary bearing stiffness and disk position on the bifurcation behavior of a magnetically supported coaxial rotor system in auxiliary bearings.

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 aim of this study is to develop a thyristor model based on the general equations of the semiconductors.

Within the theory of the systems, the paper starts with the identification of the regenerative feedback current loop present in the p‐n‐p‐n structures. By using phase‐plane analysis and bifurcation theory, it analyses the stability of the different states of the devices and, at the same time, identifies the different characteristic critical points. The analysis of the non‐homogeneous solutions which can bifurcate from the uniform carrier distributions in the thyristor bases gives a further insight about the nature of the switching process.

A link between the electric bistable characteristics of thyristors and their physical and geometrical properties was found.

The main implication of this work is the acquisition of a method to implement a thyristor model for circuit analysis purposes where the different model parameters can be extracted from the respective device data sheets by using analytical methods.

The simulation of some particular characteristics of the thyristor by numerical methods has been described in other original works of the authors for the non‐homogeneous case. Here, the search is mainly to apply some of the more important findings of the work to a first‐level lumped thyristor model to be used in circuit analysis applications.

This paper aims to present a literature review on analytical research on the prediction of aircraft spin and recovery characteristics, as it progressed from the early years of aviation to current state of the art spin technologies.

Aerodynamic model development approaches that have been generally used in past spin studies are presented. Past contributions in application of these analytical techniques to predict spin and recovery characteristics on various fighters, general aviation and airliners are discussed, thus providing useful reference for researchers embarking aircraft spin research. An overview of the development of spin prevention and spin recovery technologies to mitigate stall/spin susceptibility is presented.

The challenges associated with the presented techniques that prompt possible future research directions are discussed.

Despite considerable progress in the recent years, no comprehensive review on the analytical and computational research techniques to predict aircraft post-stall/ spin characteristics has been undertaken in the recent years.

The purpose of this paper is to present a numerical analysis of the nonlinear dynamic response of a gear‐bearing system subject to nonlinear suspension effects, micropolar fluid, journal bearing, nonlinear oil‐film force and nonlinear gear mesh force. The results presented in this study provide some useful insights into the design and development of the system for rotating machinery that operates in highly rotational speed and highly nonlinear regimes.

The non‐dimensional equation of the gear‐bearing system proposed in this study is solved using the Runge‐Kutta method. The non‐periodic behavior of this system is characterized using phase diagrams, power spectra, Poincaré maps, bifurcation diagrams, Lyapunov exponents and the fractal dimension of the system.

The numerical results reveal that the system exhibits a diverse range of periodic, sub‐harmonic, quasi‐periodic and chaotic behaviors. The micropolar fluid is a useful lubricating fluid to suppress nonlinear dynamic responses and improve the dynamic regularity of the systems.

The unbalance coefficient, damping coefficient, other control parameters and some experiments are also important to identify dynamic behaviors of those systems and they may be regarded as research directions in the future.

Because of financial constraints, some important experiments are outstanding to identify dynamic behaviors of these systems and await research in the future.

This study has presented a numerical analysis of the nonlinear dynamic response of a gear‐bearing system with nonlinear suspension effects, micropolar fluid, journal bearing, nonlinear oil‐film force and nonlinear gear mesh force.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.