Nonlinear dynamics of phase-locked discrete coupled systems

We investigate numerically and analytically the nonlinear dynamics of a system consisting of two self-synchronizing pulse-coupled nonlinear oscillators with delay. The particular system considered consists of connected digital phase-locked loops. We find mapping equations that govern the system and determine the synchronization properties. We study the bifurcation diagrams, which show regions of periodic, quasiperiodic and chaotic behavior, with unusual bifurcation diagrams, depending on the delay. We show that depending on the parameter that is varied, the delay will have a synchronizing or desynchronizing effect on the locked state. The stability of the system is studied by determining the Liapunov exponents, indicating marked differences compared to coupled systems without delay.

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Nonlinear dynamics of coupled systems near magnetic phase transitions of the “order-order” type

Journal of Magnetism and Magnetic Materials ◽

10.1016/0304-8853(91)90840-7 ◽

1991 ◽

Vol 100 (1-3) ◽

pp. 544-571 ◽

Cited By ~ 43

Author(s):

V.I. Ozhogin ◽

V.L. Preobrazhenskii

Keyword(s):

Nonlinear Dynamics ◽

Phase Transitions ◽

Magnetic Phase ◽

Order Type ◽

Coupled Systems ◽

Magnetic Phase Transitions

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UNCERTAINTY QUANTIFICATION OF THE NONLINEAR DYNAMICS OF ELECTROMECHANICAL COUPLED SYSTEMS

Proceedings of the 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering – COMPDYN 2013 ◽

10.7712/120113.4647.c1039 ◽

2014 ◽

Author(s):

R. de Queiroz Lima ◽

R. Sampaio

Keyword(s):

Nonlinear Dynamics ◽

Uncertainty Quantification ◽

Coupled Systems ◽

Electromechanical Coupled

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Nonlinear Dynamics and Chaos in Micro/Nano-Scale Systems and Applications

Additional Conferences (Device Packaging HiTEC HiTEN & CICMT) ◽

10.4071/2016dpc-wp34 ◽

2016 ◽

Vol 2016 (DPC) ◽

pp. 001588-001612

Author(s):

Ying-Cheng Lai

Keyword(s):

Nonlinear Dynamics ◽

Silicon Nanowires ◽

Microelectromechanical Systems ◽

Anomalous Hall Effect ◽

Spatiotemporal Chaos ◽

Coupled Systems ◽

Nanoelectromechanical Systems ◽

Nonlinear Dynamics And Chaos ◽

Potential Applications ◽

Oscillator Arrays

Microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS) are characterized by their small size, extremely low power consumption, and ultra fast speed. Recent years have witnessed a growing interest in the fundamental nonlinear dynamics of MEMS/NEMS and their potential applications. The Nonlinear Dynamics group at Arizona State University carried out a series of studies to investigate nonlinear dynamics and chaos in MEMS/NEMS on topics such as inducing chaos in MEMS, spatiotemporal chaos and intrinsic localized motions in MEMS oscillator arrays, extensive chaos in electrostatically driven silicon nanowires, and multistability and anomalous Hall effect in ferromagnet-topological insulator coupled systems. An overview of these results will be presented.

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Complexity and Nonlinear Dynamics in Psychotherapy

European Review ◽

10.1017/s1062798709000763 ◽

2009 ◽

Vol 17 (2) ◽

pp. 331-356 ◽

Cited By ~ 20

Author(s):

Günter Schiepek

Keyword(s):

Nonlinear Dynamics ◽

Human Life ◽

Social Systems ◽

Learning Processes ◽

Coupled Systems ◽

Self Organization ◽

Life Changes ◽

Changing Patterns ◽

Development Processes

Human life changes with time. It seems therefore obvious that most of the phenomena that psychology and psychotherapy are concerned with are dynamic in nature. For human development processes, human change and learning processes, the dynamics and prognosis of mental disorders, problems manifesting in social systems such as couples, families, teams, or the question of how psychotherapy works, self-organization is ubiquitous. In the context of self-organization, complexity is a quality of changing patterns and patterns of change, produced by nonlinear coupled systems.

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