Bifurcation and Chaos in Fuzzy Dynamical Systems
From Fundamentals to Applications in Uncertain Environments
Buch in deiner Nähe kaufen
Beschreibung
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 α-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.
In addition, this book:
- Highlights emerging research directions and identifies open problems and potential avenues for future investigation
- Offers a distinctive perspective by bridging uncertainty modeling with the complex dynamics of nonlinear systems
- Examines how fuzzy uncertainty can be systematically incorporated into nonlinear dynamical models
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 α-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.
Highlights emerging research directions and identifies open problems and potential avenues for future investigation Offers a distinctive perspective by bridging uncertainty modeling with the complex dynamics of nonlinear systems Examines how fuzzy uncertainty can be systematically incorporated into nonlinear dynamical models
Autor*in
Snehashish Chakraverty
Themen in »Bifurcation and Chaos in Fuzzy Dynamical Systems«
Fuzzy Dynamical Systems Bifurcation and Chaos Theory Nonlinear Systems with Uncertainty Chaos in Fuzzy Models Modeling Uncertainty in Complex Systems