Mathematical Marvels: Texts and Monographs in the Spirit of CR Rao – serie

This book is devoted to the study of the global properties of the dynamical systems. It gives a justification of using numerical methods for solving several problems such as localization of a chain-recurrent set of trajectories, construction of attractors and their domains of attraction, construction of filtrations, calculation of invariant measures, approximation of ergodic measures, estimation of the entropy of a dynamical system, calculation of the averaging spectrum of a function, calculation of the Morse spectrum, a test for the hyperbolicity of a dynamical system. The book is intended for researchers in dynamical systems and their applications in many scientific and technical disciplines, including engineering, physics, chemistry, biology, economics, and demography.

This textbook is written with the intention of providing the essentials of foundational training in modeling, both mathematical and stochastic. It offers a comprehensive understanding of theoretical and formal mathematical demography and human population dynamics. Presented in an engaging, clear and concise manner, it aims to outline traditional material and recent advancements in the field, specifically tailored for both beginners and professionals. Separate chapters discuss classical as well as recent developments in stable and stationary populations, such as Euler–Lotka population equations, and life tables. Partial differential equations models of single population dynamics, McKendrick von Foerster models of population growth and Okubo’s diffusion models are derived. Population ecology models like the Lotka–Volterra two-population framework, Kermack–McKendrick three-population models, and their stability analysis foundations are succinctly explained. Recent advancements in stationary population theories and newer population stability principles developed are included. The book also includes two chapters on stochastic process models in demography. The content of the book is not only accessible and relevant to students and researchers in mathematical demography but also to those working in actuarial science, ecology, statistics and mathematical modeling.