Mathematical Modelling of Complex Patterns Through Fractals and Dynamical Systems

This book offers a wide range of interesting correlations beyond the domains of dynamical systems, complex systems, and fractal geometry. Exploring complex systems and their properties using the fractal approaches, this book provides initial solutions for new areas where fractal theory has yet to verify its

expertise. Further, the book focusses on the latest scientific interest and illustrates general fractal theory in multidisciplinary areas such as computer science, electronics engineering, electrical engineering, bioengineering, biomedical, quantum physics and fluid dynamics research. This edited book is designed for professionals in the field of mathematics, computer science and physics, and even for non-specialists to help understand the concepts of fractals in nonlinear dynamical systems and complex systems while offering applications for researchers in the pure as well as in the applied background of science and

engineering.

Offers interesting correlations beyond the domains of dynamical systems, complex systems, and fractal geometry Provides initial solutions for new areas where fractal theory has yet to verify its expertise Serves as a reference for professionals in the field of mathematics, computer science and physics

Autorentext

A. Gowrisankar received his PhD degree (in Mathematics) from the Gandhigram Rural Institute (Deemed

to be University), Gandhigram, Dindigul, India, in 2017. He was a postdoctoral fellow at the Indian Institute of Technology Guwahati (IITG), Guwahati, Assam, India, in 2017. He is the Assistant Professor in the Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India, with five years of experience. His broad research areas include Fractal Analysis, Image

Processing, Fractal Interpolation Functions, Fractional Calculus, Nonlinear Dynamics and Climate Change. He has published over 25 research articles in reputed international journals and two books in CRC Press, 2019 and Springer: Complexity, 2021. He was one of the editors for two edited books in CRC Press, Taylor & Francis Group (in 2022 and another in the process). He was the guest editor for two special issues in The European Physical Journal Special Topics, Springer. He has been the reviewer for more than 10 international journals and was awarded "Distinguished EPJ Referees -2021".

Kishore Bingi received the B.Tech. Degree in Electrical and Electronics Engineering from Acharya

Nagarjuna University, India, in 2012. He received the M.Tech. Degree in Instrumentation and Control

Systems from the National Institute of Technology Calicut, India, in 2014, and a PhD in Electrical and

Electronic Engineering from Universiti Teknologi PETRONAS, Malaysia, in 2019. From 2014 to 2015, he

worked as an Assistant Systems Engineer at TATA Consultancy Services Limited, India. From 2019 to 2020, he worked as Research Scientist and Post-Doctoral Researcher at the Universiti Teknologi PETRONAS, Malaysia. From 2020 to 2022, he served as an Assistant Professor at the Process Control Laboratory, School of Electrical Engineering, Vellore Institute of Technology, India. Since 2022 he has been working as a faculty member at the Department of Electrical and Electronic Engineering at Universiti Teknologi PETRONAS, Malaysia. His research area is developing fractional-order neural networks, including fractional-order systems and controllers, chaos prediction and forecasting, and advanced hybrid optimization techniques. He is an IEEE and IET Member and a registered Chartered Engineer (CEng) from Engineering Council UK. He serves as an Editorial Board Member for the International Journal of Applied Mathematics and Computer Science and Academic Editor for Mathematical Problems in Engineering and the Journal of Control Science and Engineering.

Cristina Serpa has a degree in Applied Mathematics - Fundamental Applications, a Master's and a PhD in

Mathematics, in Mathematical Analysis, from the Faculty of Sciences of the University of Lisbon. She is an invited associate professor in the Mathematics Department of the Instituto Superior de Engenharia de Lisboa of the Instituto Politécnico de Lisboa.Her teaching duties are usually focused on calculus curricular units for engineering. She is an integrated member of CMAFcIO - Center for Mathematics, Fundamental Applications and Operational Research, of the University of Lisbon and collaborates with the Portuguese Mathematical Society. He researches Fractals at the fundamental theoretical level and in the context of their applications. He created the Fractal Regression method, developing corresponding software to obtain fractal functions from real data.

Inhalt

Exploring Initial Value Problems in Fractal Delay Equations.- Multi-Level Fractal Analysis with Applications.- Topological Indices on Fractal Patterns.- The Smoothness of Multifractal Hewitt-Stromberg Dimensions.- Bivariate Rational Fractal Model with Function Values.- Epidemiology Analysis.- Nonlinear Thermal Radiation in Dynamic Energy Systems.- : Dynamic Queueing System with Time Based Uncertainty.- Dynamical Properties of Constant Uncertainty System with Optimization.- Dynamical Systems and its Complexity.- Fractal-Based Time Series Modelling.- Fractal Approaches to Climate Dynamics.