Search Results (3)

In this research paper, we study symmetry groups, soliton solutions, and the dynamical behavior of the Ivancevic Option Pricing Model (IOPM). First, we find the Lie symmetries of the considered model; next, we use them to determine the corresponding symmetry groups. Then, we attempt to solve IOPM by means of two methods. We provide some wave solutions and give further details of the solution using 2D and 3D graphs. These results are interpreted as important clarifications in financial mathematics and deepen our understanding of the dynamics involved during the pricing of options. Secondly, the quasi-periodic behavior of the two-dimensional dynamical system and its perturbed system are plotted using Python software (Python 3.13.5 version). Various frequencies and amplitudes are considered to confirm the quasi-periodic behavior via the Lyapunov exponent, bifurcation diagram, and multistability analysis. These findings are particularly in consonance with current research that investigates IOPM as a nonlinear wave alternate for normal models and the importance of graphical representations in the understanding of financial derivative dynamics. We, therefore, hope to fill in the gaps in the literature that currently exist about the use of multi-solution methods and their effects on financial modeling through the employment of sophisticated graphical techniques. This will be helpful in discussing matters in the field of financial mathematics and open up new directions of investigation. Full article

Currently, despite advances in the analysis of dynamical systems, there are still doubts about the transition between both stable and chaotic behaviors. In this research, we will explain the transition of a system that develops between two dynamic systems that have already been studied: the classical logistic model and a new chaotic system. This research addresses the study of the transition of both the system and its behaviors using computational techniques, where cobweb diagrams, time series, bifurcation diagrams, and even a graphical visualization for the maximum Lyapunov exponent will be visualized. Using a graphical and numerical methodology, bifurcation points were identified that revealed the transition of behaviors at different points. This resulted in a deep understanding of the dynamics of the system, thus highlighting the importance of incorporating computational analysis in dynamic systems, which greatly contributes to the efficient modeling of natural phenomena. Full article

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. Full article