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This textbook provides an accessible introduction to the theory and applications of dynamical systems, with a balanced treatment of discrete-time and continuous models. Beginning with core modelling principles, the book develops the mathematical tools needed to analyse qualitative behaviour, including fixed points, stability, oscillations, and long-term dynamics. One-dimensional discrete and continuous systems are explored in detail before extending the discussion to multi-variable models, where richer behaviours emerge. Special attention is given to bifurcations and transitions between dynamical regimes, highlighting their role in parameter-dependent models. The final chapters introduce the geometric structures underlying chaotic dynamics, including fractals and strange attractors. Throughout, the emphasis is on clear exposition, intuitive reasoning, and the use of dynamical systems to understand real-world phenomena.
Dr Bakhtier Vasiev has been working at a number of universities and research centres across Europe, including the Universities of Utrecht (Netherlands), Munich (Germany) and Dundee (Scotland). His research was supported by the Alexander von Humbold fellowship award and a number of research grants from EPSRC and BBSRC. Since 2014, Dr Vasiev has been a senior lecturer in the Department of Mathematical Sciences at the University of Liverpool. His research is focused on mathematical aspects of nonlinear dynamics and pattern formation in biological systems with an emphasis on biological development and aging. He has contributed to the mathematical modelling of a number of biological processes including numerical and analytical studies.