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- Title
- Numerical Investigation of Finite Kuramoto model with time dependent coupling strength.
- Creator
- Khatiwada, Dharma Raj, Wille, Luc T., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Physics
- Abstract/Description
-
Synchronization of an ensemble of oscillators is a phenomenon present in systems of different fields, ranging from social and physical to biological and technological systems. The most successful approach to describe how synchrony emerges in these systems is given by the Kuramoto model. This model as it stands, however, assumes oscillators of fixed natural frequencies and a homogeneous all-to-all coupling strength. The Kuramoto model has been analytically discussed to address the...
Show moreSynchronization of an ensemble of oscillators is a phenomenon present in systems of different fields, ranging from social and physical to biological and technological systems. The most successful approach to describe how synchrony emerges in these systems is given by the Kuramoto model. This model as it stands, however, assumes oscillators of fixed natural frequencies and a homogeneous all-to-all coupling strength. The Kuramoto model has been analytically discussed to address the synchronization phenomena of coupled oscillators in the thermodynamic limit (N --> ∞). However, there needs to be a modi cation to address the inevitable in uence of external fields on the pattern of various real life synchronization phenomena which, in general; involves a finite number of oscillators. This research introduces a time dependent coupling strength K(t) which is from the modulation of external elds in the form of, for example, a periodic impulse, in the nite oscillators assembly. A sinusoidal function with some arbitrary values of amplitude and frequency is added to the fixed coupling strength as a perturbation of external elds. Temporal evolution of order parameter r(t) and phase θ(t), both of which measure the degree of synchronization of an assembly of oscillators simultaneously, are compared between uniform and time dependent cases. Graphical comparison are made using a 2 oscillator system, a building block of any finite oscillators case. Also, similar comparisons are performed for a system of 32 oscillators which are chosen randomly as a representative of a nite number of oscillators (2 < N < ∞). A temporal variation of the relative phase angle θ(t) = θ2(t) - θ1(t) in 2 and 32 oscillators systems using uniform and time dependent cases is also a part of this research. This work also introduces a time-dependent coupling strength in the form of a step function. The main objective of using such a function is to keep the synchronized behavior of the oscillators persistently. This behavior can be achieved with the perception that occasional boosting with higher coupling strength K(t) should be enough to sustain synchronous behavior of oscillators which, in general, are tuned with lower K(t).
Show less - Date Issued
- 2018
- PURL
- http://purl.flvc.org/fau/fd/FA00013120
- Subject Headings
- Synchronization, Oscillations, Nonlinear oscillators--Mathematical models, Oscillator strengths, Frequency of oscillating systems
- Format
- Document (PDF)
- Title
- Simulations and feedback control of nonlinear coupled electromechanical oscillators for energy conversion applications.
- Creator
- Psarrou, Dimitrios., Dhanak, Manhar R., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
- Abstract/Description
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This thesis discusses the coupling of a mechanical and electrical oscillator, an arrangement that is often encountered in mechatronics actuators and sensors. The dynamics of this coupled system is mathematically modeled and a low pass equivalent model is presented. Numerical simulations are then performed, for various input signals to characterize the nonlinear relationship between the electrical current and the displacement of the mass. Lastly a framework is proposed to estimate the mass...
Show moreThis thesis discusses the coupling of a mechanical and electrical oscillator, an arrangement that is often encountered in mechatronics actuators and sensors. The dynamics of this coupled system is mathematically modeled and a low pass equivalent model is presented. Numerical simulations are then performed, for various input signals to characterize the nonlinear relationship between the electrical current and the displacement of the mass. Lastly a framework is proposed to estimate the mass position without the use of a position sensor, enabling the sensorless control of the coupled system and additionally providing the ability for the system to act as an actuator or a sensor. This is of value for health monitoring, diagnostics and prognostics, actuation and power transfer of a number of interconnected machines that have more than one electrical system, driving corresponding mechanical subsystems while being driven by the same voltage source and at the same time being spectrally separated and independent.
Show less - Date Issued
- 2011
- PURL
- http://purl.flvc.org/FAU/3320109
- Subject Headings
- Renewable energy sources, Mechatronics, Nonlinear theories, Oscillators, System analysis
- Format
- Document (PDF)
- Title
- The influence of connectivity on the global dynamics of nonlinear oscillator ensembles.
- Creator
- Rogers, Jeffrey L., Florida Atlantic University, Wille, Luc T.
- Abstract/Description
-
In this thesis we have studied the global dynamics which spontaneously emerge in ensembles of interacting disparate nonlinear oscillators. Collective phenomena exhibited in these systems include synchronization, quasiperiodicity, chaos, and death. Exact analytical solutions are presented for two and three coupled oscillators with phase and amplitude variations. A phenomenon analogous to a phase-transition is found as a function of interaction-range in a one-dimensional lattice: for coupling...
Show moreIn this thesis we have studied the global dynamics which spontaneously emerge in ensembles of interacting disparate nonlinear oscillators. Collective phenomena exhibited in these systems include synchronization, quasiperiodicity, chaos, and death. Exact analytical solutions are presented for two and three coupled oscillators with phase and amplitude variations. A phenomenon analogous to a phase-transition is found as a function of interaction-range in a one-dimensional lattice: for coupling exponents larger than some critical value, alpha c, synchronization is shown to be impossible. Massively parallel computer simulations in conjunction with finite-size scaling were used to extrapolate to the infinite-size limit.
Show less - Date Issued
- 1994
- PURL
- http://purl.flvc.org/fcla/dt/15031
- Subject Headings
- Nonlinear oscillators, Coupled mode theory, Physics--Data processing, Parallel processing (Electronic computers)
- Format
- Document (PDF)