Beginning with realistic mathematical or verbal models of physical or biological phenomena, the author derives tractable mathematical models that are amenable to further mathematical analysis or to elucidating computer simulations. For the most part, derivations are based on perturbation methods. Because of this, the majority of the text is devoted to careful derivations of implicit function theorems, the method of averaging, and quasi-static state approximation methods. The duality between stability and perturbation is developed and used, relying heavily on the concept of stability under persistent disturbances. This explains why stability results developed for quite simple problems are often useful for more complicated, even chaotic, ones. Relevant topics about linear systems, nonlinear oscillations, and stability methods for difference, differential-delay, integro- differential and ordinary and partial differential equations are developed throughout the book. For the second edition, the author has restructured the chapters, placing special emphasis on introductory materials in Chapters 1 and 2 as distinct from presentation materials in Chapters 3 through 8. In addition, more material on bifurcations from the point of view of canonical models, sections on randomly perturbed systems, and several new computer simulations have been added.

Land deterioration, drought, desertification, and water resources shrinkage threaten natural resources, negatively impacting environmental, economic, and political stability. The increasing occurrence of climate change (extremes) impacts land degradation processes, soil erosion by water and wind, and salinization. The researchers have invested several years of scientific research in natural resources deterioration, including soil degradation and erosion, land degradation, desertification, and climate changes, which are interesting enough. However, the link between science and policymaking appears to be less active as serious actions do not take fast. The eighteen chapters of this book focus more on topics related to natural resources deterioration, such as land degradation, desertification, drought, climate change, and analysis of numerous case studies.

This groundbreaking book delves into the dynamic interplay between human activities and the environment, offering a nuanced understanding of how land-use decisions shape our world. In this volume experts from diverse fields converge to present a comprehensive exploration of the latest developments in land-use practices.