This paper uncovers some striking and new complex phenomena in a memristive diode bridge-based Murali–Lakshmanan–Chua (MLC) circuit. These striking dynamical behaviors include the coexistence of multiple attractors and double-transient chaos. Also, period-doubling, chaos, crisis scenarios are observed in the system when varying the amplitude of the external excitation. Numerical simulation tools like phase portrait, cross-section basin of attraction, Lyapunov spectrum, bifurcation diagrams and time series are used to highlight the complex dynamical behaviors in the memristive system. Further, practical realizations of the circuit both in PSpice and real-laboratory measurements match well with the observed numerical simulations.

The presence of a high ripple in the inductor current of a DC-DC converter in a photovoltaic converter chain leads to a considerable decrease in the energy efficiency of the converter. To solve this problem, we consider a current-mode control and for economic reasons we used a single inductor current sensor with a low-pass filter. The purpose of the low-pass filter is to minimize the effect of ripple in the inductor current by taking only the DC component of the signal at the output of the sensor for tracking the maximum power point. The objective of this paper is therefore to study the stability of the photovoltaic system as a function of the filter frequency while maintaining a good power level. First, we propose a general modeling of the whole system by linearizing the PV around the maximum power point. Floquet theory is used to determine analytically the stability of the overall system. The fourth-order Runge–Kutta method is used to plot bifurcation diagrams and Lyapunov exponents in MATLAB/SIMULINK when the filter frequency varies in a limited range and the ramp amplitude is taken as a control parameter. Secondly, the PSIM software is used to design the device and validate the results obtained in MATLAB/SIMULINK. The results depicted in MATLAB/SIMULINK are in perfect agreement with those obtained in PSIM. We found that not only is the energy level maintained at the maximum power level of 85.17 W, but also that the stability range of the photovoltaic system increased with the value of the filter cut-off frequency. This research offers a wider range of parameters for stability control of photovoltaic systems contrarily to others found in literature.

By means of Liapounov's method, we establish a sufficient condition for stability of a nonlinear pendulum.Методом Ляпунова знайдено достатню умову стiйкостi руху нелiнiйного маятника.

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