This paper investigates the impact of bifurcations on the performance of power electronic circuits. We focus on circuits that include energy-harvesting devices, which exhibit a maximum power point (MPP). In particular, a DC–DC converter with a photovoltaic (PV) module is considered a representative example of such systems to evaluate the relationship between the circuit performance indices (such as power conversion and maximum power point tracking (MPPT) efficiency) and the bifurcation phenomena observed in the system. First, experimental results are reported that evaluate circuit characteristics and performance under MPPT control. Then, a novel mathematical PV model is presented and fully defined using experimentally measured parameters; this model does not necessitate the use of root-finding algorithms. Next, this model is integrated with the switched nonlinear model of a DC–DC converter subject to peak current mode control (PCMC), and a stability analysis of the periodic orbits is performed. Finally, the relationship between circuit performance and observed bifurcation phenomena is investigated and discussed. This research demonstrates the occurrence of both period-doubling and Neimark–Sacker bifurcations in the system considered here, and these features are shown in a two-parameter bifurcation diagram.

The current-mode controlled DC-DC boost converter with photovoltaic module is studied in this paper. First, we show the circuit model, and explain the circuit dynamics. Next, a stability analysis method based on the monodromy matrix is shown. Finally, we investigate nonlinear phenomena in the circuit from both of numerical and experimental points of view.

This study proposes a novel derivative-free-optimization-based bifurcation point detection strategy that automatically adjusts parameter settings during the search. The proposed method is based on an adaptive differential evolution (JADE) and does not require parameter tuning by the user. Simulation results show that the proposed method obtains accurate bifurcation parameter sets with a higher success rate and a shorter time than the classic DE. Furthermore, we investigate the influence of the population size on the performance, and the proposed method requires fewer populations than DE. By using the proposed method, the user obtains a two-parameter bifurcation diagram without the derivative of the objective function or the careful setting of the simulation parameters.

In this paper, we propose a numerical method to calculate the grazing bifurcation points in an impact oscillator with periodic boundaries. First, we illustrate the n-dimensional autonomous impact oscillator with the moving boundaries. The boundaries consist of the scalar function involving the periodic function. When the trajectory hits one boundary, the solution jumps to the other immediately. Next, we construct the composite Poincaré map and show its derivatives. Using the derivatives, we calculate the location of the periodic point, bifurcation parameter and time that elapses before the trajectory hitting the boundary. Finally, we apply the method to a Rayleigh-type oscillator with the sinusoidal boundaries to confirm its validity.

We propose the occasional delayed feedback control for chaotic circuits with interrupt characteristics. The control input generated by the difference between the current state and the delayed state is added to the system occasionally, i.e., during a certain interval defined by the switching policy. This control is reasonable for chaotic systems including some switches since they are not always feasible to admit the control input, e.g., a fixed control input terminal may be separated according to the switching action. We apply the control method to a chaotic switched circuit and demonstrate availability by some numerical experiments.

This paper proposes switch synchronizing delayed feedback control (abbr. SSDFC) in the piecewise linear systems. This control method weeds out the unsuitable control input from the different piecewise continuous functions. As an illustrated example, we then apply this general methodology to a simple circuit containing state-period dependent switch. The unstable periodic orbit is stabilized effectively in the computer simulations. Finally, the performance of SSDFC is compared with delayed feedback control (DFC)

This paper considers a system interrupted by own state and a periodic interval. We know this system has prospects of occurrence of border-collision bifurcation. To analyze properties of the dynamics, we derive a one-dimensional map explicitly. We show some theorems and the existence of regions of periodic solution within two-parameter space. Some theoretical results are verified by laboratory experiments.