Nonlinear Dynamics in Complex Systems Via Fractals and Fractional Calculus
Title | Nonlinear Dynamics in Complex Systems Via Fractals and Fractional Calculus PDF eBook |
Author | Viorel-Puiu Paun |
Publisher | Mdpi AG |
Pages | 0 |
Release | 2023-08-16 |
Genre | |
ISBN | 9783036583365 |
Current advances in the knowledge of nonlinear dynamical networks, systems and processes, as well as their unified repercussions, allow us to include some typical complex natural phenomena, from the nanoscale to an extra-galactic scale, in an unitarian comprehensive manner. In other words, the physical, biological and financial data, as well as technological ones (mechanical or electronic devices), of complex systems available today can be managed by the same unique conceptual approach, both analytically and through a computer simulation, using effective nonlinear dynamics procedures. This volume collected some important advances in the fields of fractal curves, fractal analysis and fractional calculus, as well as new solutions of fractal differential equations. The works edited in the present technical publication are those that appeared in the Fractal and Fractional journal, in a Special Issue of the same name.
Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems
Title | Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems PDF eBook |
Author | Yeliz Karaca |
Publisher | Academic Press |
Pages | 352 |
Release | 2022-06-22 |
Genre | Science |
ISBN | 0323886167 |
Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems addresses different uncertain processes inherent in the complex systems, attempting to provide global and robust optimized solutions distinctively through multifarious methods, technical analyses, modeling, optimization processes, numerical simulations, case studies as well as applications including theoretical aspects of complexity. Foregrounding Multi-chaos, Fractal and Multi-fractional in the era of Artificial Intelligence (AI), the edited book deals with multi- chaos, fractal, multifractional, fractional calculus, fractional operators, quantum, wavelet, entropy-based applications, artificial intelligence, mathematics-informed and data driven processes aside from the means of modelling, and simulations for the solution of multifaceted problems characterized by nonlinearity, non-regularity and self-similarity, frequently encountered in different complex systems. The fundamental interacting components underlying complexity, complexity thinking, processes and theory along with computational processes and technologies, with machine learning as the core component of AI demonstrate the enabling of complex data to augment some critical human skills. Appealing to an interdisciplinary network of scientists and researchers to disseminate the theory and application in medicine, neurology, mathematics, physics, biology, chemistry, information theory, engineering, computer science, social sciences and other far-reaching domains, the overarching aim is to empower out-of-the-box thinking through multifarious methods, directed towards paradoxical situations, uncertain processes, chaotic, transient and nonlinear dynamics of complex systems. Constructs and presents a multifarious approach for critical decision-making processes embodying paradoxes and uncertainty. Includes a combination of theory and applications with regard to multi-chaos, fractal and multi-fractional as well as AI of different complex systems and many-body systems. Provides readers with a bridge between application of advanced computational mathematical methods and AI based on comprehensive analyses and broad theories.
Recent Advances in Applied Nonlinear Dynamics with Numerical Analysis
Title | Recent Advances in Applied Nonlinear Dynamics with Numerical Analysis PDF eBook |
Author | Changpin Li |
Publisher | World Scientific |
Pages | 414 |
Release | 2013 |
Genre | Science |
ISBN | 9814436461 |
Nonlinear dynamics is still a hot and challenging topic. In this edited book, we focus on fractional dynamics, infinite dimensional dynamics defined by the partial differential equation, network dynamics, fractal dynamics, and their numerical analysis and simulation.Fractional dynamics is a new topic in the research field of nonlinear dynamics which has attracted increasing interest due to its potential applications in the real world, such as modeling memory processes and materials. In this part, basic theory for fractional differential equations and numerical simulations for these equations will be introduced and discussed.In the infinite dimensional dynamics part, we emphasize on numerical calculation and theoretical analysis, including constructing various numerical methods and computing the corresponding limit sets, etc.In the last part, we show interest in network dynamics and fractal dynamics together with numerical simulations as well as their applications.
Nonlinear and Complex Dynamics
Title | Nonlinear and Complex Dynamics PDF eBook |
Author | José António Tenreiro Machado |
Publisher | Springer Science & Business Media |
Pages | 328 |
Release | 2011-08-28 |
Genre | Technology & Engineering |
ISBN | 146140231X |
Nonlinear Dynamics of Complex Systems describes chaos, fractal and stochasticities within celestial mechanics, financial systems and biochemical systems. Part I discusses methods and applications in celestial systems and new results in such areas as low energy impact dynamics, low-thrust planar trajectories to the moon and earth-to-halo transfers in the sun, earth and moon. Part II presents the dynamics of complex systems including bio-systems, neural systems, chemical systems and hydro-dynamical systems. Finally, Part III covers economic and financial systems including market uncertainty, inflation, economic activity and foreign competition and the role of nonlinear dynamics in each.
Fractional-Order Nonlinear Systems
Title | Fractional-Order Nonlinear Systems PDF eBook |
Author | Ivo Petráš |
Publisher | Springer Science & Business Media |
Pages | 218 |
Release | 2011-05-30 |
Genre | Technology & Engineering |
ISBN | 3642181015 |
"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. Ivo Petráš is an Associate Professor of automatic control and the Director of the Institute of Control and Informatization of Production Processes, Faculty of BERG, Technical University of Košice, Slovak Republic. His main research interests include control systems, industrial automation, and applied mathematics.
Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors
Title | Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors PDF eBook |
Author | Christos Volos |
Publisher | MDPI |
Pages | 290 |
Release | 2019-05-03 |
Genre | Technology & Engineering |
ISBN | 3038978981 |
In recent years, entropy has been used as a measure of the degree of chaos in dynamical systems. Thus, it is important to study entropy in nonlinear systems. Moreover, there has been increasing interest in the last few years regarding the novel classification of nonlinear dynamical systems including two kinds of attractors: self-excited attractors and hidden attractors. The localization of self-excited attractors by applying a standard computational procedure is straightforward. In systems with hidden attractors, however, a specific computational procedure must be developed, since equilibrium points do not help in the localization of hidden attractors. Some examples of this kind of system are chaotic dynamical systems with no equilibrium points; with only stable equilibria, curves of equilibria, and surfaces of equilibria; and with non-hyperbolic equilibria. There is evidence that hidden attractors play a vital role in various fields ranging from phase-locked loops, oscillators, describing convective fluid motion, drilling systems, information theory, cryptography, and multilevel DC/DC converters. This Special Issue is a collection of the latest scientific trends on the advanced topics of dynamics, entropy, fractional order calculus, and applications in complex systems with self-excited attractors and hidden attractors.
New Perspectives on Nonlinear Dynamics and Complexity
Title | New Perspectives on Nonlinear Dynamics and Complexity PDF eBook |
Author | Dimitri Volchenkov |
Publisher | Springer Nature |
Pages | 198 |
Release | 2022-07-29 |
Genre | Technology & Engineering |
ISBN | 303097328X |
This book presents select, recent developments in nonlinear and complex systems reported at the 1st Online Conference on Nonlinear Dynamics and Complexity, held on November 23-25, 2020. It provides an exchange recent developments, discoveries, and progresses in Nonlinear Dynamics and Complexity. The collection presents fundamental and frontier theories and techniques for modern science and technology, stimulates more research interest for exploration of nonlinear science and complexity; and passes along new knowledge and insight to the next generation of engineers and technologists in a range of fields.