Symmetry in Chaotic Systems and Circuits

Symmetry can play an important role in the field of nonlinear systems and especially in the design of nonlinear circuits that produce chaos. Therefore, this Special Issue, titled “Symmetry in Chaotic Systems and Circuits”, presents the latest scientific advances in nonlinear chaotic systems and circuits that introduce various kinds of symmetries. Applications of chaotic systems and circuits with symmetries, or with a deliberate lack of symmetry, are also presented in this Special Issue. The volume contains 14 published papers from authors around the world. This reflects the high impact of this Special Issue

Entropy in Dynamic Systems

In order to measure and quantify the complex behavior of real-world systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor, and control complicated chaotic and stochastic processes. Though the term of entropy comes from Greek and emphasizes its analogy to energy, today, it has wandered to different branches of pure and applied sciences and is understood in a rather rough way, with emphasis placed on the transition from regular to chaotic states, stochastic and deterministic disorder, and uniform and non-uniform distribution or decay of diversity. This collection of papers addresses the notion of entropy in a very broad sense. The presented manuscripts follow from different branches of mathematical/physical sciences, natural/social sciences, and engineering-oriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and anti-synchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed

Mathematical and Numerical Aspects of Dynamical System Analysis

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”

Dynamical Systems

Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and electrical and mechanical structures. Complex systems are often composed of a large number of interconnected and interacting entities, exhibiting much richer global scale dynamics than the properties and behavior of individual entities. Complex systems are studied in many areas of natural sciences, social sciences, engineering and mathematical sciences. This special issue therefore intends to contribute towards the dissemination of the multifaceted concepts in accepted use by the scientific community. We hope readers enjoy this pertinent selection of papers which represents relevant examples of the state of the art in present day research. [...

Education Reform at the "Edge of Chaos": Constructing ETCH (An Education Theory Complexity Hybrid) for an Optimal Learning Education Environment

EDUCATION REFORM AT THE "EDGE OF CHAOS":CONSTRUCTING ETCH (AN EDUCATION THEORY COMPLEXITY HYBRID) FOR AN OPTIMAL LEARNING EDUCATION ENVIRONMENT AbstractCurrently, the theoretical foundation that inspires educational theory, which in turn shapes the systemic structure of institutions of learning, is based on three key interconnected, interacting underpinnings -mechanism, reductionism, and linearity. My dissertation explores this current theoretical underpinning including its fallacies and inconsistencies, and then frames an alternative educational theoretical base - a hybrid complex adaptive systems theory model for education - that more effectively meets the demands to prepare students for the 21st century. My Education Theory Complexity Hybrid (ETCH) differs by focusing on the systemic, autopoietic nature of schools, the open, fluid processes of school systems as a dissipative structure, and nonlinearity or impossibility of completely predicting the results of any specific intervention within a school system.. In addition, I show how ETCH principles, when applied by educational system leaders, permit them to facilitate an optimal learning environment for a student-centered complex adaptive system.ETCH is derived from Complexity Theory and is a coherent, valid, and verifiable systems' framework that accurately aligns the education system with its goal as a student-centered complex adaptive system. In contrast to most dissertations in the School Leadership Program, which are empirical studies, mine explores this new theoretical orientation and illustrates the power of that orientation through a series of examples taken from my experiences in founding and operating the Lancaster Institute for Learning, a private state-licensed alternative high school in eastern Pennsylvania