Predicting incipent instabilities and bifurcations of nonlinear dynamical systems modelling compliant off-shore structures

For engineers, the two most important aspects of dynamical analysis are high amplitude resonance vibrations and structural stability, i.e. whether a steady state solution is stable under small perturbations. For the former case, a novel and simple method based on Poincare mapping technique has been devised to predict an imminent flip bifurcation. This bifurcation represents the beginning of the second order subharmonic response. For the latter case, we discovered that while classical quantitative analytical techniques work well in establishing the 'local' structural stability of a steady state solution, the global geometric structure of the catchment region can alter dramatically such that even an initial condition close to the steady state can diverge from it rather than being attracted. This phenomenon known as fractal basin boundary occurs when the invariant manifolds of the saddle separating the steady state solution from any remote attractor cross. The critical point in which the invariant manifolds just touch can be accurately predict by the Melinkov's method. Because of the complicated interwoven nature of the invariant manifolds, it is called a tangle. If the invariant manifolds are originated from the same saddle, the crossing is known as a homoclinic tangle, if originated from different saddle, a heteroclinic tangle. The critical point is then known as homoclinic or heteroclinic tangency. Tangles are also intimately related to chaotic behaviour. The creation and destruction of chaotic attractors have been observed through a series of homoclinic and heteroclinic tangency. In fact, after the invariant manifolds of an inverting saddle cross, the unstable manifold becomes the chaotic attractor. This leads us to believe that all chaotic attractors are topologically the same

Nonlinear dynamics of new magneto-mechanical oscillator

Funding Information: ZH and DW acknowledge the financial supports of CSC (China Scholarship Council) and the Shandong Province Natural Science Foundation, China (No. ZR2017BA031 , ZR2017QA005 ), the National Natural Science Foundation of China (No. 11702111 , 11732014 ). The authors also thank Drs Dimitri Costa and Vahid Vaziri for their experimental support. Publisher Copyright: © 2021 Elsevier B.V.Peer reviewedPostprin

The Kuramoto model: A simple paradigm for synchronization phenomena

Synchronization phenomena in large populations of interacting elements are the subject of intense research efforts in physical, biological, chemical, and social systems. A successful approach to the problem of synchronization consists of modeling each member of the population as a phase oscillator. In this review, synchronization is analyzed in one of the most representative models of coupled phase oscillators, the Kuramoto model. A rigorous mathematical treatment, specific numerical methods, and many variations and extensions of the original model that have appeared in the last few years are presented. Relevant applications of the model in different contexts are also included

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”

Vibration, Control and Stability of Dynamical Systems

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”