Bifurcation and Chaos in Fuzzy Dynamical Systems

From Fundamentals to Applications in Uncertain Environments
Erscheinungsjahr 2026
ISBN: 978-3-032-41988-0
Verlag: Springer

Buch, Englisch, 141 Seiten, Format (B × H): 168 mm x 240 mm

Reihe: Synthesis Lectures on Mathematics & Statistics

This book provides readers with a clear and accessible introduction to fuzzy dynamical systems, bifurcation, and chaotic behavior. By bridging mathematical foundations with systematic analysis, the authors present the essential concepts and tools required to investigate nonlinear dynamical systems under fuzzy uncertainty. The book discusses how uncertainty in system parameters and initial conditions can be represented through intervals/fuzzy numbers and analyzed using the a-cut and double-parametric representations. Beginning with the foundations of dynamical systems and fuzzy sets, the discussion develops a unified framework for fuzzy bifurcation analysis, phase-space evolution, and chaotic dynamics while preserving the underlying governing differential equations. The proposed methodology is illustrated through canonical saddle-node, transcritical, pitchfork, and Hopf bifurcations, together with phase-space analyses and the Lorenz chaotic system. In addition to theoretical developments, the book includes worked examples, bifurcation diagrams, phase portraits, trajectory families, and computational illustrations that strengthen conceptual understanding. The methods and ideas presented are relevant across disciplines such as applied mathematics, engineering, physics, biology, and environmental science, and the book also enhances the capacity to apply these techniques in diverse scientific and professional contexts. This book offers graduate learners, young academics, and emerging researchers with an accessible introduction to the interplay between fuzzy uncertainty, nonlinear dynamical systems, bifurcation phenomena, and chaotic dynamics.

Zielgruppe

Professional/practitioner

Autoren/Hrsg.

Chakraverty, Snehashish

Sahoo, Mrutyunjaya

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz

Inhaltsverzeichnis

An Overview of Dynamical Systems with Uncertainty.- Basics of Fuzzy Set Theory and Bifurcation Analysis.- Fuzzy Ordinary Differential Equations and Bifurcation Analysis.- Fuzzy Partial Differential Equations and Complex Dynamics.- Measuring and Detecting Chaos in Fuzzy Models.- Real-World Applications and Emerging Frontiers.

Über Autor(innen)

Snehashish Chakraverty, Ph.D., is a Professor in the Department of Mathematics at the National Institute of Technology Rourkela, India.  He is a globally recognized academician and researcher with over 30 years of experience in the fields of mathematical modeling, structural mechanics, uncertainty quantification, and computational methods.  Dr. Chakraverty has authored more than 35 books and 340 peer-reviewed journal articles published by reputed publishers.  He has also served as the editor and editorial board member of numerous international journals and has received numerous national and international awards for his contributions to mathematical modeling and applied mechanics.  His recent research spans soft computing, AI techniques in mechanics, and computational modeling of smart structures.

Mrutyunjaya Sahoo, Ph.D., is an Assistant Professor at the Center of Data Science, Institute of Technical Education and Research (ITER), SOA University, Bhubaneswar, India.  He received his Ph.D. from the Department of Mathematics at the National Institute of Technology Rourkela, India, and holds an M.Phil. in Mathematics and an M.Sc. in Mathematics and Computing.  His research advances both theoretical and computational methodologies for nonlinear dynamical systems, with a particular focus on bridging classical and uncertain (fuzzy) modeling frameworks. Dr. Sahoo has published multiple research articles and book chapters, along with peer-reviewed conference papers, and has presented his work at several national and international conferences and workshops.He has also served as a reviewer for several reputed national and international journals.