Current Search: Nonlinear Dynamics. (x)
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 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 intermediatesized (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 HakenKelsoBunz model (for large and smallscale coordination respectively) by adding the secondorder 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 dataanalytic tool was developed to quantify complex metastable patterns based on their topological features. The recurrence of topological features revealed important structures and transitions in highdimensional dynamic patterns that eluded its nontopological counterparts. Taken together, the work has paved the way for a deeper understanding of multiscale coordinative structures.
Show less  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)
 Title
 TIME EVOLUTION OF TRUNCATED SOLITONS ACCORDING TO THE KORTEWEGDE VRIES EQUATION.
 Creator
 ERICKSON, GARY MICHAEL., Florida Atlantic University
 Abstract/Description

The longtime behavior of the solution for x >> t^1/3 of the Kortewegde Vries equation is found when the initial data consists of a right or lefttruncated 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)
 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)
 Title
 Dynamics and Control of Autonomous Underwater Vehicles with Internal Actuators.
 Creator
 Li, Bo, Su, TsungChow, 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 highperformance 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 highperformance 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 bodyfluid dynamical system in an ideal fluid are derived using both NewtonEuler 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 horizontalplane motion of the vehicle is inherently unstable. The yaw moment exerted by the relative flow is destabilizing. The openloop stabilities of the horizontalplane 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 horizontalplane 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 horizontalplane 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 closedloop horizontalplane and verticalplane motions are also analyzed.
Show less  Date Issued
 2016
 PURL
 http://purl.flvc.org/fau/fd/FA00004738, http://purl.flvc.org/fau/fd/FA00004738
 Subject Headings
 Dynamics., Remote submersiblesDesign and construction., Ocean engineering., Fluid dynamics., Nonlinear control theory., Differentiable dynamical systems.
 Format
 Document (PDF)
 Title
 Developing combinatorial multicomponent 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
 20070830
 PURL
 http://purl.flvc.org/fau/165790
 Subject Headings
 Drug Therapy, Biomathematics, Combinatorial dynamics, DrugsResearch, MedicineMathematics, BiophysicsResearch, Nonlinear systems
 Format
 Document (PDF)
 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 threedimensional vector field possessing an inclinationflip 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 threedimensional vector field possessing an inclinationflip 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.
Show less  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)
 Title
 Dynamics of twoactor cooperation–competition conflict models.
 Creator
 Liebovitch, Larry S., Naudot, Vincent, Vallacher, Robin R., Nowak, Andrzej, BuiWrzosinska, Lan, Coleman, Peter T.
 Date Issued
 20081101
 PURL
 http://purl.flvc.org/fau/165475
 Subject Headings
 Nonlinear theories, Social systemsMathematical models, Conflict management, Cooperativeness, Differential equations, Competition, DynamicsMathematical models
 Format
 Document (PDF)
 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.
Show less  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)
 Title
 Stability analysis for singularly perturbed systems with timedelays.
 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)