Dynamical system theory has developed rapidly over the past fifty years. It is a subject upon which the theory of limit cycles has a significant impact for both theoretical advances and practical solutions to problems. Hopf bifurcation from a center or a focus is integral to the theory of bifurcation of limit cycles, for which normal form theory is a central tool. Although Hopf bifurcation has been studied for more than half a century, and normal form theory for over 100 years, efficient computation in this area is still a challenge with implications for Hilbert's 16th problem.

This book introduces the most recent developments in this field and provides major advances in fundamental theory of limit cycles. Split into two parts, the first focuses on the study of limit cycles bifurcating from Hopf singularity using normal form theory with later application to Hilbert's 16th problem, while the second considers near Hamiltonian systems using Melnikov function as the main mathematical tool.

Classic topics with new results are presented in a clear and concise manner and are accompanied by the liberal use of illustrations throughout. Containing a wealth of examples and structured algorithms that are treated in detail, a good balance between theoretical and applied topics is demonstrated. By including complete Maple programs within the text, this book also enables the reader to reconstruct the majority of formulas provided, facilitating the use of concrete models for study.

Through the adoption of an elementary and practical approach, this book will be of use to graduate mathematics students wishing to study the theory of limit cycles as well as scientists, across a number of disciplines, with an interest in the applications of periodic behavior."

Following the recent developments in the field of absolute stability, Prof. Xiaoxin Liao, in conjunction with Prof. Pei Yu, has created a second edition of his seminal work on the subject. Liao begins with an introduction to the Lurie problem and Lurie control system, before moving on to the simple algebraic sufficient conditions for the absolute stability of autonomous and non-autonomous ODE systems, as well as several special classes of Lurie-type systems. The focus of the book then shifts toward the new results and research that have appeared in the decade since the first edition was published. This book is aimed to be used by undergraduates in the areas of applied mathematics, nonlinear control systems, and chaos control and synchronisation, but may also be useful as a reference for researchers and engineers. The book is self-contained, though a basic knowledge of calculus, linear system and matrix theory, and ordinary differential equations is a prerequisite.

Following the recent developments in the field of absolute stability, Prof. Xiaoxin Liao, in conjunction with Prof. Pei Yu, has created a second edition of his seminal work on the subject. Liao begins with an introduction to the Lurie problem and Lurie control system, before moving on to the simple algebraic sufficient conditions for the absolute stability of autonomous and non-autonomous ODE systems, as well as several special classes of Lurie-type systems. The focus of the book then shifts toward the new results and research that have appeared in the decade since the first edition was published. This book is aimed to be used by undergraduates in the areas of applied mathematics, nonlinear control systems, and chaos control and synchronisation, but may also be useful as a reference for researchers and engineers. The book is self-contained, though a basic knowledge of calculus, linear system and matrix theory, and ordinary differential equations is a prerequisite.

Dynamical system theory has developed rapidly over the past fifty years. It is a subject upon which the theory of limit cycles has a significant impact for both theoretical advances and practical solutions to problems. Hopf bifurcation from a center or a focus is integral to the theory of bifurcation of limit cycles, for which normal form theory is a central tool. Although Hopf bifurcation has been studied for more than half a century, and normal form theory for over 100 years, efficient computation in this area is still a challenge with implications for Hilbert's 16th problem.

This book introduces the most recent developments in this field and provides major advances in fundamental theory of limit cycles. Split into two parts, the first focuses on the study of limit cycles bifurcating from Hopf singularity using normal form theory with later application to Hilbert's 16th problem, while the second considers near Hamiltonian systems using Melnikov function as the main mathematical tool.

Classic topics with new results are presented in a clear and concise manner and are accompanied by the liberal use of illustrations throughout. Containing a wealth of examples and structured algorithms that are treated in detail, a good balance between theoretical and applied topics is demonstrated. By including complete Maple programs within the text, this book also enables the reader to reconstruct the majority of formulas provided, facilitating the use of concrete models for study.

Through the adoption of an elementary and practical approach, this book will be of use to graduate mathematics students wishing to study the theory of limit cycles as well as scientists, across a number of disciplines, with an interest in the applications of periodic behavior."

Driven by the advent of two-dimensional materials, valleytronics is emerging as the next hot field of research in materials science. While the use of charge or spin degrees of freedom in electronic materials as information carriers is familiar and well-appreciated, employment of the valley degree of freedom as an information carrier has remained elusive for many decades. Shortly following the discovery of isolated graphene, 2D semiconductors such as transition metal dichalcogenides were also isolated and investigated. We now understand that these materials can have separately addressable valleys because each valley can be uniquely coupled to a spin state. This imparts the ability to address different valleys (like pseudospins) with electric field, magnetic field, or light, and there is now a real possibility to engineer practical devices based on using valley as the information carrier.Valleytronics in 2D Materials is the first book in the world on the topic of valleytronics. The reader is introduced to the concept via a brief history emphasizing the challenges that impeded its development for so long. We then dive into the valley physics of 2D semiconductors to explain the recent excitement in 2D valleytronics, the scientific investigations to confirm the addressable valleys, and the attempts to engineer valley devices for practical purposes. The text takes on a decidedly practical approach towards the subject, seeking to bring the reader quickly into the field by presenting the minimum theoretical basis for understanding the use of the valley degree of freedom in devices. A selection of key works establishing the scientific underpinnings of valley addressability and control are described to help the reader grasp the current stage of understanding, the technical foundations established, and the open questions. The renewal in valleytronics is yet unfinished, but with more than a decade of research and engineering efforts devoted in recent times, this book seeks to provide a timely reference for students, scientists and engineers to join this exciting journey and perhaps help to create the next disruption in information technology.

The Association for the Study of Play (ASP) is the sponsor of the seventh volume in the Play and Culture Studies Series. The ASP is a professional group of researchers who study play. The purpose of this series is to advance knowledge about play and culture. Volume seven presents current theoretical and empirical research on play and culture from a variety of disciplines including psychology, education, and sociology. The book begins with an overview of the twentieth-century and moves from conceptualizing play to significant and timely topics, such as the relationship between play and literacy. Applications to practice and policy implications are presented and include play with action figures; playgrounds; play as an integral part of the human experience; and the value of play with books for toddlers. Research activity and interests of contemporary play scholars are highlighted and discussed in relation to projected problems and needs facing us as we enter the new millennium, such as childhood obesity; play as a venue for social interaction; and play as a method of developing skill for interaction at the local and national levels as adults.