What kind of dynamics is a piecewise linear system able to display? How may they generate heteroclinic chaos? How can the coexistence of attractors be designed and characterized? Is it necessary to have equilibrium points to generate chaotic behavior? Chaos theory and complex systems are interesting and evolving topics whose investigation from a theoretical and practical point of view constantly leads to arising questions. Interesting behaviors can be observed in self-excited attractors, hidden attractors and non-self-excited attractors. This book presents some fundamentals of linear system theory and recent approaches to design the three classes of chaotic attractors in piecewise linear systems. Each chapter presents a brief description and basic concepts to provide an overview of linear systems theory; chaos and multistability in integer linear systems; hidden and non-self-excited attractors; and fractional approaches. They also provide example systems to illustrate the concepts and design methods introduced. Some current topics under investigation are addressed from an integer order perspective to make the connection with the fractional order counterpart. This textbook provides a comprehensive introduction, methodologies, and analysis tools to study chaotic piecewise linear systems and will be suitable for undergraduate or graduate students interested in the field of chaos and complex dynamics.
Eric Campos Cantón is Professor in the Division of control and dynamical systems, Instituto Potosino de investigación Científica y tecnológica A.C., Mexico, and head of the Nonlinear and Chaotic Dynamics Laboratory. He is a member of the Researches National System, Mexico (CONACYT). He edited the book "Complex Systems and Their Applications" (Springer, 2022). As of 2022, He has been Associate Editor for Journal of Applied Nonlinear Dynamics (L&H Scientific Publishing), Frontiers in Applied Mathematics and Statistics (Frontier). He has also been academic editor for Mathematical Problems in Engineering, and Complexity since 2018, and Member of the scientific committee of the journal "Informador Técnico del SENA Centro ASTIN de Cali" since 2013. He was guest editor for special issues "Open Challenges on the Stability of Complex Systems: Insights of Nonlinear Phenomena with or without Delay" (Complexity, 2019), "New Trends on Modeling, Design, and Control of Chaotic Systems" (Mathematical Problems in Engineering, 2017), "Preservation of relevant properties of interconnected dynamical systems over complex network", (Journal of the Franklin Institute, 2013), and "Complex discrete dynamics and its structures in bioinspired systems", (Discrete Dynamics in Nature and Society, 2013).
Rodolfo de Jesús Escalante González is professor at Electrical, Electronics and Mechatronics Department, Technological Institute of San Luis Potosí, Mexico. He is a member of the Researches National System, Mexico (CONACYT).
Héctor Eduardo Gilardi Velízquez is professor at Facultad de Ingeniería, Universidad Panamericana Campus Aguascalientes, Mexico. He is a member of the Researches National System, Mexico (CONACYT)
