Marek Berezowski Bücher

Focusing on the mathematical modeling of chemical reactors, this study delves into the complex behaviors generated by differential equations, including steady states and chaotic oscillations. It emphasizes the analysis of chaotic phenomena and fractals, utilizing concepts such as bifurcation, Lyapunov's exponent, and power spectrum. The author presents various methods for addressing these challenges, showcasing results through bifurcation diagrams and phase planes. This work builds upon previous research, offering new insights into the predictability of chaos in chemical processes.

Is our brain a computer? Are we able to understand the brain? What is consciousness? Do algorithms think? Is mathematics omnipotent? Can it generate works of art? Can we calculate the Mandelbrot fractal? Do bicycle wheels draw fractals? What may aliens be like? Could we communicate with aliens? Why is the theory of relativity incomprehensible? Is "the twin paradox" really a paradox? What do we need complex numbers for? Is number 1 unique? To get the answers, I would like invite readers to my book.

The heart of most chemical plants is a chemical reactor. They are described by system of differential equations. Each of these models can generate complex solutions, including: multiple steady states, periodic oscillations, quasiperiodic oscillations or chaos. Analysis of this equations requires the use of sophisticated mathematical methods and complex numerical algorithms. In this study these phenomena and methods of analysis were presented. Particular attention is paid to the bifurcation problems, chaotic oscillations and fractals. Different methods were presented which were used to solve above mention problems. The following concepts as: bifurcation, Lyapunov's exponent, Lyapunov's time and power spectrum were used for this purpose. Presentation of these phenomena on bifurcation diagrams and phase planes give fractal images. This study is based on the author's own research cycle.

This book presents a set of fractals, which were created as a visualization of the scientific results of the author on the nonlinear dynamics. This collection has been divided into three parts due to the three mathematical models. The first part refers to the complex hyperbole raised to the square. The second part refers to the complex variable has been raised to the complex variable. The third part based on mathematical models of the chemical reactor. Fractal images created by the author have not only aesthetic value. They also allow the evaluation of the sensitivity and stability of the model.