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The Coordination Dynamics of Multiple Agents
Title
The Coordination Dynamics of Multiple Agents.
Creator
Zhang, Mengsen, Tognoli, Emmanuelle, Kelso, J. A. Scott, Florida Atlantic University, Charles E. Schmidt College of Science, Center for Complex Systems and Brain Sciences
Abstract/Description
A fundamental question in Complexity Science is how numerous dynamic processes coordinate with each other on multiple levels of description to form a complex whole - a multiscale coordinative structure (e.g. a community of interacting people, organs, cells, molecules etc.). This dissertation includes a series of empirical, theoretical and methodological studies of rhythmic coordination between multiple agents to uncover dynamic principles underlying multiscale coordinative structures. First,...
Show moreA fundamental question in Complexity Science is how numerous dynamic processes coordinate with each other on multiple levels of description to form a complex whole - a multiscale coordinative structure (e.g. a community of interacting people, organs, cells, molecules etc.). This dissertation includes a series of empirical, theoretical and methodological studies of rhythmic coordination between multiple agents to uncover dynamic principles underlying multiscale coordinative structures. First, a new experimental paradigm was developed for studying coordination at multiple levels of description in intermediate-sized (N = 8) ensembles of humans. Based on this paradigm, coordination dynamics in 15 ensembles was examined experimentally, where the diversity of subjects movement frequency was manipulated to induce di erent grouping behavior. Phase coordination between subjects was found to be metastable with inphase and antiphase tendencies. Higher frequency diversity led to segregation between frequency groups, reduced intragroup coordination, and dispersion of dyadic phase relations (i.e. relations at di erent levels of description). Subsequently, a model was developed, successfully capturing these observations. The model reconciles the Kuramoto and the extended Haken-Kelso-Bunz model (for large- and small-scale coordination respectively) by adding the second-order coupling from the latter to the former. The second order coupling is indispensable in capturing experimental observations and connects behavioral complexity (i.e. multistability) of coordinative structures across scales. Both the experimental and theoretical studies revealed multiagent metastable coordination as a powerful mechanism for generating complex spatiotemporal patterns. Coexistence of multiple phase relations gives rise to many topologically distinct metastable patterns with di erent degrees of complexity. Finally, a new data-analytic tool was developed to quantify complex metastable patterns based on their topological features. The recurrence of topological features revealed important structures and transitions in high-dimensional dynamic patterns that eluded its non-topological counterparts. Taken together, the work has paved the way for a deeper understanding of multiscale coordinative structures.
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Date Issued
2018
PURL
http://purl.flvc.org/fau/fd/FA00013111
Subject Headings
Complexity science, Coordination dynamics, Nonlinear Dynamics, Nonlinear systems and complexity
Format
Document (PDF)
TIME EVOLUTION OF TRUNCATED SOLITONS ACCORDING TO THE KORTEWEG-DE VRIES EQUATION
Title
TIME EVOLUTION OF TRUNCATED SOLITONS ACCORDING TO THE KORTEWEG-DE VRIES EQUATION.
Creator
ERICKSON, GARY MICHAEL., Florida Atlantic University
Abstract/Description
The long-time behavior of the solution for x >> t^1/3 of the Korteweg-de Vries equation is found when the initial data consists of a right or left-truncated soliton. The initial data in either case is found to evolve into a complete soliton of smaller amplitude. The amplitude, velocity, and phase shift of the resultant soliton is explicitly given, and the emergence of this soliton from the initial disturbance is described in both cases.
Date Issued
1978
PURL
http://purl.flvc.org/fcla/dt/13950
Subject Headings
Solitons, Plasma dynamics, Nonlinear waves, Wave equation
Format
Document (PDF)
PARAMETERIZATION OF INVARIANT CIRCLES IN MAPS
Title
PARAMETERIZATION OF INVARIANT CIRCLES IN MAPS.
Creator
Blessing, David Charles, James, J. D. James, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
Abstract/Description
We explore a novel method of approximating contractible invariant circles in maps. The process begins by leveraging improvements on Birkhoff's Ergodic Theorem via Weighted Birkhoff Averages to compute high precision estimates on several Fourier modes. We then set up a Newton-like iteration scheme to further improve the estimation and extend the approximation out to a sufficient number of modes to yield a significant decay in the magnitude of the coefficients of high order. With this...
Show moreWe explore a novel method of approximating contractible invariant circles in maps. The process begins by leveraging improvements on Birkhoff's Ergodic Theorem via Weighted Birkhoff Averages to compute high precision estimates on several Fourier modes. We then set up a Newton-like iteration scheme to further improve the estimation and extend the approximation out to a sufficient number of modes to yield a significant decay in the magnitude of the coefficients of high order. With this approximation in hand, we explore the phase space near the approximate invariant circle with a form numerical continuation where the rotation number is perturbed and the process is repeated. Then, we turn our attention to a completely different problem which can be approached in a similar way to the numerical continuation, finding a Siegel disk boundary in a holomorphic map. Given a holomorphic map which leads to a formally solvable cohomological equation near the origin, we use a numerical continuation style process to approximate an invariant circle in the Siegel disk near the origin. Using an iterative scheme, we then enlarge the invariant circle so that it approximates the boundary of the Siegel disk.
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Date Issued
2024
PURL
http://purl.flvc.org/fau/fd/FA00014464
Subject Headings
Dynamical systems, Nonlinearity (Mathematics), Numerical analysis, Parameterization
Format
Document (PDF)
Dynamics of social coordination: the synchronization of internal states in close relationships
Title
Dynamics of social coordination: the synchronization of internal states in close relationships.
Creator
Vallacher, Robin R., Nowak, Andrzej, Zochowski, Michal
Date Issued
2005
PURL
http://purl.flvc.org/fcla/dt/2182034
Subject Headings
Dynamics., Psychology, Social., Interpersonal relations --Mathematical models., Interpersonal relations --Psychological aspects., Psychometrics., Nonlinear Dynamics.
Format
Document (PDF)
Dynamics and Control of Autonomous Underwater Vehicles with Internal Actuators
Title
Dynamics and Control of Autonomous Underwater Vehicles with Internal Actuators.
Creator
Li, Bo, Su, Tsung-Chow, Florida Atlantic University, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description
This dissertation concerns the dynamics and control of an autonomous underwater vehicle (AUV) which uses internal actuators to stabilize its horizontalplane motion. The demand for high-performance AUVs are growing in the field of ocean engineering due to increasing activities in ocean exploration and research. New generations of AUVs are expected to operate in harsh and complex ocean environments. We propose a hybrid design of an underwater vehicle which uses internal actuators instead of...
Show moreThis dissertation concerns the dynamics and control of an autonomous underwater vehicle (AUV) which uses internal actuators to stabilize its horizontalplane motion. The demand for high-performance AUVs are growing in the field of ocean engineering due to increasing activities in ocean exploration and research. New generations of AUVs are expected to operate in harsh and complex ocean environments. We propose a hybrid design of an underwater vehicle which uses internal actuators instead of control surfaces to steer. When operating at low speeds or in relatively strong ocean currents, the performances of control surfaces will degrade. Internal actuators work independent of the relative ows, thus improving the maneuvering performance of the vehicle. We develop the mathematical model which describes the motion of an underwater vehicle in ocean currents from first principles. The equations of motion of a body-fluid dynamical system in an ideal fluid are derived using both Newton-Euler and Lagrangian formulations. The viscous effects of a real fluid are considered separately. We use a REMUS 100 AUV as the research model, and conduct CFD simulations to compute the viscous hydrodynamic coe cients with ANSYS Fluent. The simulation results show that the horizontal-plane motion of the vehicle is inherently unstable. The yaw moment exerted by the relative flow is destabilizing. The open-loop stabilities of the horizontal-plane motion of the vehicle in both ideal and real fluid are analyzed. In particular, the effects of a roll torque and a moving mass on the horizontal-plane motion are studied. The results illustrate that both the position and number of equilibrium points of the dynamical system are prone to the magnitude of the roll torque and the lateral position of the moving mass. We propose the design of using an internal moving mass to stabilize the horizontal-plane motion of the REMUS 100 AUV. A linear quadratic regulator (LQR) is designed to take advantage of both the linear momentum and lateral position of the internal moving mass to stabilize the heading angle of the vehicle. Alternatively, we introduce a tunnel thruster to the design, and use backstepping and Lyapunov redesign techniques to derive a nonlinear feedback control law to achieve autopilot. The coupling e ects between the closed-loop horizontal-plane and vertical-plane motions are also analyzed.
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Date Issued
2016
PURL
http://purl.flvc.org/fau/fd/FA00004738, http://purl.flvc.org/fau/fd/FA00004738
Subject Headings
Dynamics., Remote submersibles--Design and construction., Ocean engineering., Fluid dynamics., Nonlinear control theory., Differentiable dynamical systems.
Format
Document (PDF)
Developing combinatorial multi-component therapies (CMCT) of drugs that are more specific and have fewer side effects than traditional one drug therapies
Title
Developing combinatorial multi-component therapies (CMCT) of drugs that are more specific and have fewer side effects than traditional one drug therapies.
Creator
Liebovitch, Larry S., Tsinoremas, Nicholas, Pandya, Abhijit S.
Date Issued
2007-08-30
PURL
http://purl.flvc.org/fau/165790
Subject Headings
Drug Therapy, Biomathematics, Combinatorial dynamics, Drugs--Research, Medicine-Mathematics, Biophysics--Research, Nonlinear systems
Format
Document (PDF)
Nonlinear Phenomena from a Reinjected Horseshoe
Title
Nonlinear Phenomena from a Reinjected Horseshoe.
Creator
Fontaine, Marcus, Kalies, William D., Naudot, Vincent, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description
A geometric model of a reinjected cuspidal horseshoe is constructed, that resembles the standard horseshoe, but where the set of points that escape are now reinjected and contribute to richer dynamics. We show it is observed in the unfolding of a three-dimensional vector field possessing an inclination-flip homoclinic orbit with a resonant hyperbolic equilibrium. We use techniques from classical dynamical systems theory and rigorous computational symbolic dynamics with algebraic topology to...
Show moreA geometric model of a reinjected cuspidal horseshoe is constructed, that resembles the standard horseshoe, but where the set of points that escape are now reinjected and contribute to richer dynamics. We show it is observed in the unfolding of a three-dimensional vector field possessing an inclination-flip homoclinic orbit with a resonant hyperbolic equilibrium. We use techniques from classical dynamical systems theory and rigorous computational symbolic dynamics with algebraic topology to show that for suitable parameters the flow contains a strange attractor.
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Date Issued
2016
PURL
http://purl.flvc.org/fau/fd/FA00004591
Subject Headings
Nonlinear theories., Computational dynamics., Attractors (Mathematics), Chaotic behavior in systems., Mathematical physics.
Format
Document (PDF)
Dynamics of two-actor cooperation–competition conflict models
Title
Dynamics of two-actor cooperation–competition conflict models.
Creator
Liebovitch, Larry S., Naudot, Vincent, Vallacher, Robin R., Nowak, Andrzej, Bui-Wrzosinska, Lan, Coleman, Peter T.
Date Issued
2008-11-01
PURL
http://purl.flvc.org/fau/165475
Subject Headings
Nonlinear theories, Social systems--Mathematical models, Conflict management, Cooperativeness, Differential equations, Competition, Dynamics--Mathematical models
Format
Document (PDF)
Nonlinearity and entrepreneurship
Title
Nonlinearity and entrepreneurship.
Creator
Pflaum, Blaine., Harriet L. Wilkes Honors College
Abstract/Description
Entrepreneurship occupies a curious place in economic theory. On one hand, the importance of entrepreneurship is widely recognized, particularly as it pertains to economic growth. However, the entrepreneur lacks a broadly accepted economic theory, and suffers from a dearth of literature on the subject. We believe that this is due to economics' heavy reliance on linear mathematical theory. In this thesis, we use nonlinear mathematics to construct a model of the entrepreneur that captures the...
Show moreEntrepreneurship occupies a curious place in economic theory. On one hand, the importance of entrepreneurship is widely recognized, particularly as it pertains to economic growth. However, the entrepreneur lacks a broadly accepted economic theory, and suffers from a dearth of literature on the subject. We believe that this is due to economics' heavy reliance on linear mathematical theory. In this thesis, we use nonlinear mathematics to construct a model of the entrepreneur that captures the sudden destabilization of a steady state, the unpredictability of a creative action, the possibility of entrepreneurial failure, and sensitivity to small changes in environment.
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Date Issued
2010
PURL
http://purl.flvc.org/FAU/3335458
Subject Headings
Economics, Mathematical, Nonlinear theories, Entrepreneurship, Mathematical models, New business enterprises, Econometric models, Statics and dynamics (Social sciences)
Format
Document (PDF)
Stability analysis for singularly perturbed systems with time-delays
Title
Stability analysis for singularly perturbed systems with time-delays.
Creator
Yang, Yang, Wang, Yuan, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description
Singularly perturbed systems with or without delays commonly appear in mathematical modeling of physical and chemical processes, engineering applications, and increasingly, in mathematical biology. There has been intensive work for singularly perturbed systems, yet most of the work so far focused on systems without delays. In this thesis, we provide a new set of tools for the stability analysis for singularly perturbed control systems with time delays.
Date Issued
2015
PURL
http://purl.flvc.org/fau/fd/FA00004423, http://purl.flvc.org/fau/fd/FA00004423
Subject Headings
Biology -- Mathematical models, Biomathematics, Differentiable dynamical systems, Differential equations, Partial -- Numerical solutions, Global analysis (Mathematics), Lyapunov functions, Nonlinear theories
Format
Document (PDF)