Numerical bifurcation analysis of maps. From theory to software. This book combines a comprehensive state-of-the-art analysis of bifurcations of discrete-time dynamical systems with concrete instruction on implementations (and example applications) in the free MATLAB software MatContM developed by the authors. While self-contained and suitable for independent study, the book is also written with users in mind and is an invaluable reference for practitioners. Part I focuses on theory, providing a systematic presentation of bifurcations of fixed points and cycles of finite-dimensional maps, up to and including cases with two control parameters. Several complementary methods, including Lyapunov exponents, invariant manifolds and homoclinic structures, and parts of chaos theory, are presented. Part II introduces MatContM through step-by-step tutorials on how to use the general numerical methods described in Part I for simple dynamical models defined by one- and two-dimensional maps. Further examples in Part III show how MatContM can be used to analyze more complicated models from modern engineering, ecology, and economics.
Keywords for this software
References in zbMATH (referenced in 8 articles , 1 standard article )
Showing results 1 to 8 of 8.
- Naik, Parvaiz Ahmad; Eskandari, Zohreh; Yavuz, Mehmet; Zu, Jian: Complex dynamics of a discrete-time Bazykin-Berezovskaya prey-predator model with a strong Allee effect (2022)
- Zhang, Limin; Xu, Yike; Liao, Guangyuan: Codimension-two bifurcations and bifurcation controls in a discrete biological system with weak Allee effect (2022)
- Borisov, A. V.; Tsiganov, A. V.; Mikishanina, E. A.: On inhomogeneous nonholonomic Bilimovich system (2021)
- Li, Bo; Liang, Houjun; He, Qizhi: Multiple and generic bifurcation analysis of a discrete Hindmarsh-Rose model (2021)
- Abernethy, Gavin M.: Book review of: Yu. A. Kuznetsov and H. G. E. Meijer, Numerical bifurcation analysis of maps. From theory to software (2020)
- Meiss, James: Book review of: Y. A. Kuznetsov and H. G. E. Meijer, Numerical bifurcation analysis of maps. From theory to software (2020)
- Kuznetsov, Yuri A.; Meijer, Hil G. E.: Numerical bifurcation analysis of maps. From theory to software (2019)
- Neirynck, Niels; Govaerts, Willy; Kuznetsov, Yuri A.; Meijer, Hil G. E.: Numerical bifurcation analysis of homoclinic orbits embedded in one-dimensional manifolds of maps (2018)