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Articles 1 - 16 of 16
Full-Text Articles in Dynamical Systems
Predator-Prey Dynamics With Intraspecific Competition And An Allee Effect In The Predator Population, Anne E. Yust, Erin N. Bodine
Predator-Prey Dynamics With Intraspecific Competition And An Allee Effect In The Predator Population, Anne E. Yust, Erin N. Bodine
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Computing The Optimal Path In Stochastic Dynamical Systems, Martha Bauver, Eric Forgoston, Lora Billings
Computing The Optimal Path In Stochastic Dynamical Systems, Martha Bauver, Eric Forgoston, Lora Billings
Department of Mathematics Facuty Scholarship and Creative Works
In stochastic systems, one is often interested in finding the optimal path that maximizes the probability of escape from a metastable state or of switching between metastable states. Even for simple systems, it may be impossible to find an analytic form of the optimal path, and in high- dimensional systems, this is almost always the case. In this article, we formulate a constructive methodology that is used to compute the optimal path numerically. The method utilizes finite-time Lyapunov exponents, statistical selection criteria, and a Newton-based iterative minimizing scheme. The method is applied to four examples. The first example is a …
Computing The Optimal Path In Stochastic Dynamical Systems, Martha Bauver, Eric Forgoston, Lora Billings
Computing The Optimal Path In Stochastic Dynamical Systems, Martha Bauver, Eric Forgoston, Lora Billings
Lora Billings
Computing The Optimal Path In Stochastic Dynamical Systems, Martha Bauver, Eric Forgoston, Lora Billings
Computing The Optimal Path In Stochastic Dynamical Systems, Martha Bauver, Eric Forgoston, Lora Billings
Eric Forgoston
Anthrax Models Involving Immunology, Epidemiology And Controls, Buddhi Raj Pantha
Anthrax Models Involving Immunology, Epidemiology And Controls, Buddhi Raj Pantha
Doctoral Dissertations
This dissertation is divided in two parts. Chapters 2 and 3 consider the use of optimal control theory in an anthrax epidemiological model. Models consisting system of ordinary differential equations (ODEs) and partial differential differential equations (PDEs) are considered to describe the dynamics of infection spread. Two controls, vaccination and disposal of infected carcasses, are considered and their optimal management strategies are investigated. Chapter 4 consists modeling early host pathogen interaction in an inhalational anthrax infection which consists a system of ODEs that describes early dynamics of bacteria-phagocytic cell interaction associated to an inhalational anthrax infection.
First we consider a …
A Bi-Stable Switch In Virus Dynamics Can Explain The Differences In Disease Outcome Following Siv Infections In Rhesus Macaques, Stanca Ciupe, Christopher Miller, Jonathan Forde
A Bi-Stable Switch In Virus Dynamics Can Explain The Differences In Disease Outcome Following Siv Infections In Rhesus Macaques, Stanca Ciupe, Christopher Miller, Jonathan Forde
Biology and Medicine Through Mathematics Conference
No abstract provided.
Growth Dynamics For Pomacea Maculata, Lihong Zhao, Karyn L. Sutton, Jacoby Carter
Growth Dynamics For Pomacea Maculata, Lihong Zhao, Karyn L. Sutton, Jacoby Carter
Biology and Medicine Through Mathematics Conference
No abstract provided.
Wilson-Cowan Coupled Dynamics In A Model Of The Cortico-Striato-Thalamo-Cortical Circuit, Anca R. Radulescu
Wilson-Cowan Coupled Dynamics In A Model Of The Cortico-Striato-Thalamo-Cortical Circuit, Anca R. Radulescu
Biology and Medicine Through Mathematics Conference
No abstract provided.
Robust Traveling Waves In Chains Of Simple Neural Oscillators, Stanislav M. Mintchev
Robust Traveling Waves In Chains Of Simple Neural Oscillators, Stanislav M. Mintchev
Biology and Medicine Through Mathematics Conference
No abstract provided.
Using Predator Carrying Capacity For A Pathogenic Vector-Dynamic Differential Model, Rosahn Bhattarai
Using Predator Carrying Capacity For A Pathogenic Vector-Dynamic Differential Model, Rosahn Bhattarai
Georgia State Undergraduate Research Conference
No abstract provided.
Memory Consolidation In Binary Inputs, Shateil C. French Mr., Ricardo J T Toscano
Memory Consolidation In Binary Inputs, Shateil C. French Mr., Ricardo J T Toscano
Georgia State Undergraduate Research Conference
No abstract provided.
Procesy Cieplne I Aparaty (Lab), Wojciech M. Budzianowski
Inżynieria Chemiczna Lab., Wojciech M. Budzianowski
Topological Data Analysis For Systems Of Coupled Oscillators, Alec Dunton
Topological Data Analysis For Systems Of Coupled Oscillators, Alec Dunton
HMC Senior Theses
Coupled oscillators, such as groups of fireflies or clusters of neurons, are found throughout nature and are frequently modeled in the applied mathematics literature. Earlier work by Kuramoto, Strogatz, and others has led to a deep understanding of the emergent behavior of systems of such oscillators using traditional dynamical systems methods. In this project we outline the application of techniques from topological data analysis to understanding the dynamics of systems of coupled oscillators. This includes the examination of partitions, partial synchronization, and attractors. By looking for clustering in a data space consisting of the phase change of oscillators over a …
Full State Revivals In Linearly Coupled Chains With Commensurate Eigenspectra, J. J. P. Veerman, Jovan Petrovic
Full State Revivals In Linearly Coupled Chains With Commensurate Eigenspectra, J. J. P. Veerman, Jovan Petrovic
Mathematics and Statistics Faculty Publications and Presentations
Coherent state transfer is an important requirement in the construction of quantum computer hardware. The state transfer can be realized by linear next-neighbour-coupled finite chains. Starting from the commensurability of chain eigenvalues as the general condition of periodic dynamics, we find chains that support full periodic state revivals. For short chains, exact solutions are found analytically by solving the inverse eigenvalue problem to obtain the coupling coefficients between chain elements. We apply the solutions to design optical waveguide arrays and perform numerical simulations of light propagation thorough realistic waveguide structures. Applications of the presented method to the realization of a …
Signal Velocity In Oscillator Arrays, Carlos E. Cantos, David K. Hammond, J. J. P. Veerman
Signal Velocity In Oscillator Arrays, Carlos E. Cantos, David K. Hammond, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
We investigate a system of coupled oscillators on the circle, which arises from a simple model for behavior of large numbers of autonomous vehicles. The model considers asymmetric, linear, decentralized dynamics, where the acceleration of each vehicle depends on the relative positions and velocities between itself and a set of local neighbors. We first derive necessary and sufficient conditions for asymptotic stability, then derive expressions for the phase velocity of propagation of disturbances in velocity through this system. We show that the high frequencies exhibit damping, which implies existence of well-defined signal velocities c+>0 and c−f(x−c+t) in the direction …