Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, 2018 Wojciech Budzianowski Consulting Services

#### Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

17 - Stability Analysis Of Stochastically Switching Kuramoto Networks, 2018 Georgia State University

#### 17 - Stability Analysis Of Stochastically Switching Kuramoto Networks, Ratislav Krylov, Igor Belykh Prof.

*Georgia Undergraduate Research Conference (GURC)*

Motivated by real-world networks with evolving connections, we analyze how stochastic switching affects patterns of synchrony and their stability in networks of identical Kuramoto oscillators with inertia. Stochastic dynamical networks are a useful model for many physical, biological, and engineering systems that have evolving topology, but they have proven to be difficult to work with, and the analytical results are rare. These networks have two characteristic time scales, one is associated with intrinsic dynamics of individual oscillators comprising the network, and the other corresponds to switching period of on-off connections. In the limit of fast switching, the relation between the ...

Bifurcation Analysis Of Two Biological Systems: A Tritrophic Food Chain Model And An Oscillating Networks Model, 2018 The University of Western Ontario

#### Bifurcation Analysis Of Two Biological Systems: A Tritrophic Food Chain Model And An Oscillating Networks Model, Xiangyu Wang

*Electronic Thesis and Dissertation Repository*

In this thesis, we apply bifurcation theory to study two biological systems. Main attention is focused on complex dynamical behaviors such as stability and bifurcation of limit cycles. Hopf bifurcation is particularly considered to show bistable or even tristable phenomenon which may occur in biological systems. Recurrence is also investigated to show that such complex behavior is common in biological systems.

First we consider a tritrophic food chain model with Holling functional response types III and IV for the predator and superpredator, respectively. Main attention is focused on the sta- bility and bifurcation of equilibria when the prey has a ...

The Influence Of Canalization On The Robustness Of Finite Dynamical Systems, 2018 Illinois State University

#### The Influence Of Canalization On The Robustness Of Finite Dynamical Systems, Claus Kadelka

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Modeling Influenza Outbreaks On A College Campus, 2018 University of Colorado Boulder

#### Modeling Influenza Outbreaks On A College Campus, Eli Goldwyn, Subekshya Bidari

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Combinatorial Geometry Of Threshold-Linear Networks, 2018 Illinois State University

#### Combinatorial Geometry Of Threshold-Linear Networks, Christopher Langdon

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Introducing The Fractional Differentiation For Clinical Data-Justified Prostate Cancer Modelling Under Iad Therapy, 2018 Illinois State University

#### Introducing The Fractional Differentiation For Clinical Data-Justified Prostate Cancer Modelling Under Iad Therapy, Ozlem Ozturk Mizrak

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Using Pair Approximation Methods To Analyze Behavior Of A Probabilistic Cellular Automaton Model For Intracellular Cardiac Calcium Dynamics, 2018 Loyola Marymount University

#### Using Pair Approximation Methods To Analyze Behavior Of A Probabilistic Cellular Automaton Model For Intracellular Cardiac Calcium Dynamics, Robert J. Rovetti

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Investigation Of Chaos In Biological Systems, 2018 The University of Western Ontario

#### Investigation Of Chaos In Biological Systems, Navaneeth Mohan

*Electronic Thesis and Dissertation Repository*

Chaos is the seemingly irregular behavior arising from a deterministic system. Chaos is observed in many real-world systems. Edward Lorenz’s seminal discovery of chaotic behavior in a weather model has prompted researchers to develop tools that distinguish chaos from non-chaotic behavior. In the first chapter of this thesis, I survey the tools for detecting chaos namely, Poincaré maps, Lyapunov exponents, surrogate data analysis, recurrence plots and correlation integral plots. In chapter two, I investigate blood pressure fluctuations for chaotic signatures. Though my analysis reveals interesting evidence in support of chaos, the utility such an analysis lies in a different ...

The Computational Study Of Fly Swarms & Complexity, 2018 Linfield College

#### The Computational Study Of Fly Swarms & Complexity, Austin Bebee

*Senior Theses*

A system is considered complex if it is composed of individual parts that abide by their own set of rules, while the system, as a whole, will produce non-deterministic properties. This prevents the behavior of such systems from being accurately predicted. The motivation for studying complexity spurs from the fact that it is a fundamental aspect of innumerable systems. Among complex systems, fly swarms are relatively simple, but even so they are still not well understood. In this research, several computational models were developed to assist with the understanding of fly swarms. These models were primarily analyzed by using the ...

Physical Applications Of The Geometric Minimum Action Method, 2018 The Graduate Center, City University of New York

#### Physical Applications Of The Geometric Minimum Action Method, George L. Poppe Jr.

*All Dissertations, Theses, and Capstone Projects*

This thesis extends the landscape of rare events problems solved on stochastic systems by means of the \textit{geometric minimum action method} (gMAM). These include partial differential equations (PDEs) such as the real Ginzburg-Landau equation (RGLE), the linear Schroedinger equation, along with various forms of the nonlinear Schroedinger equation (NLSE) including an application towards an ultra-short pulse mode-locked laser system (MLL).

Additionally we develop analytical tools that can be used alongside numerics to validate those solutions. This includes the use of instanton methods in deriving state transitions for the linear Schroedinger equation and the cubic diffusive NLSE.

These analytical solutions ...

Iterative Methods To Solve Systems Of Nonlinear Algebraic Equations, 2018 Western Kentucky University

#### Iterative Methods To Solve Systems Of Nonlinear Algebraic Equations, Md Shafiful Alam

*Masters Theses & Specialist Projects*

Iterative methods have been a very important area of study in numerical analysis since the inception of computational science. Their use ranges from solving algebraic equations to systems of differential equations and many more. In this thesis, we discuss several iterative methods, however our main focus is Newton's method. We present a detailed study of Newton's method, its order of convergence and the asymptotic error constant when solving problems of various types as well as analyze several pitfalls, which can affect convergence. We also pose some necessary and sufficient conditions on the function f for higher order of ...

P-46 A Periodic Matrix Model Of Seabird Behavior And Population Dynamics, 2018 Andrews University

#### P-46 A Periodic Matrix Model Of Seabird Behavior And Population Dynamics, Mykhaylo M. Malakhov, Benjamin Macdonald, Shandelle M. Henson, J. M. Cushing

*Honors Scholars & Undergraduate Research Poster Symposium Programs*

Rising sea surface temperatures (SSTs) in the Pacific Northwest lead to food resource reductions for surface-feeding seabirds, and have been correlated with several marked behavioral changes. Namely, higher SSTs are associated with increased egg cannibalism and egg-laying synchrony in the colony. We study the long-term effects of climate change on population dynamics and survival by considering a simplified, cross-season model that incorporates both of these behaviors in addition to density-dependent and environmental effects. We show that cannibalism can lead to backward bifurcations and strong Allee effects, allowing the population to survive at lower resource levels than would be possible otherwise.

Quasi-Static Nonlinear Analysis Of A Celestial Icosahedron Shaped Vacuum Lighter Than Air Vehicle, 2018 Air Force Institute of Technology

#### Quasi-Static Nonlinear Analysis Of A Celestial Icosahedron Shaped Vacuum Lighter Than Air Vehicle, Kyle D. Moore

*Theses and Dissertations*

Due to the many drawbacks associated with a traditional lighter than air vehicle (LTAV), there is a desire for a LTAV which generates lift from an internal vacuum. To date, two feasible designs (the icosahedron and the hexakis icosahedron) for this so called vacuum lighter than air vehicle (VLTAV) have been studied at the Air Force Institute of Technology (AFIT). This research looks to show the feasibility of a new design for a VLTAV, the celestial icosahedron. This research includes a boundary condition study which proves the symmetric nature of the celestial icosahedron's frame with laterally constrained and unconstrained ...

Theoretical Analysis Of Nonlinear Differential Equations, 2018 Stephen F Austin State University

#### Theoretical Analysis Of Nonlinear Differential Equations, Emily Jean Weymier

*Electronic Theses and Dissertations*

Nonlinear differential equations arise as mathematical models of various phenomena. Here, various methods of solving and approximating linear and nonlinear differential equations are examined. Since analytical solutions to nonlinear differential equations are rare and difficult to determine, approximation methods have been developed. Initial and boundary value problems will be discussed. Several linear and nonlinear techniques to approximate or solve the linear or nonlinear problems are demonstrated. Regular and singular perturbation theory and Magnus expansions are our particular focus. Each section offers several examples to show how each technique is implemented along with the use of visuals to demonstrate the accuracy ...

Reduced Models Of Point Vortex Systems In Quasigeostrophic Fluid Dynamics, 2018 University of Massachusetts Amherst

#### Reduced Models Of Point Vortex Systems In Quasigeostrophic Fluid Dynamics, Jonathan Maack

*Doctoral Dissertations*

We develop a nonequilibrium statistical mechanical description of the evolution of point vortex systems governed by either the Euler, single-layer quasigeostrophic or two-layer quasigeostrophic equations. Our approach is based on a recently proposed optimal closure procedure for deriving reduced models of Hamiltonian systems. In this theory the statistical evolution is kept within a parametric family of distributions based on the resolved variables chosen to describe the macrostate of the system. The approximate evolution is matched as closely as possible to the true evolution by minimizing the mean-squared residual in the Liouville equation, a metric which quantifies the information loss rate ...

Particle Filters For State Estimation Of Confined Aquifers, 2018 University of North Florida

#### Particle Filters For State Estimation Of Confined Aquifers, Graeme Field

*UNF Graduate Theses and Dissertations*

Mathematical models are used in engineering and the sciences to estimate properties of systems of interest, increasing our understanding of the surrounding world and driving technological innovation. Unfortunately, as the systems of interest grow in complexity, so to do the models necessary to accurately describe them. Analytic solutions for problems with such models are provably intractable, motivating the use of approximate yet still accurate estimation techniques. Particle filtering methods have emerged as a popular tool in the presence of such models, spreading from its origins in signal processing to a diverse set of fields throughout engineering and the sciences including ...

Hopf Bifurcation Analysis Of Chaotic Chemical Reactor Model, 2018 University of Central Florida

#### Hopf Bifurcation Analysis Of Chaotic Chemical Reactor Model, Daniel Mandragona

*Honors in the Major Theses*

Bifurcations in Huang's chaotic chemical reactor system leading from simple dynamics into chaotic regimes are considered. Following the linear stability analysis, the periodic orbit resulting from a Hopf bifurcation of any of the six fixed points is constructed analytically by the method of multiple scales across successively slower time scales, and its stability is then determined by the resulting final secularity condition. Furthermore, we run numerical simulations of our chemical reactor at a particular fixed point of interest, alongside a set of parameter values that forces our system to undergo Hopf bifurcation. These numerical simulations then verify our analysis ...

Rogue Rotary - Modular Robotic Rotary Joint Design, 2017 California Polytechnic State University, San Luis Obispo

#### Rogue Rotary - Modular Robotic Rotary Joint Design, Sean Wesley Murphy, Tyler David Riessen, Jacob Mark Triplett

*Mechanical Engineering*

This paper describes the design process from ideation to test validation for a singular robotic joint to be configured into a myriad of system level of robots.

On The Existence Of Bogdanov-Takens Bifurcations, 2017 Missouri State University

#### On The Existence Of Bogdanov-Takens Bifurcations, Zachary Deskin

*MSU Graduate Theses*

In bifurcation theory, there is a theorem (called Sotomayor's Theorem) which proves the existence of one of three possible bifurcations of a given system, provided that certain conditions of the system are satisfied. It turns out that there is a "similar" theorem for proving the existence of what is referred to as a Bogdanov-Takens bifurcation. The author is only aware of one reference that has the proof of this theorem. However, most of the details were left out of the proof. The contribution of this thesis is to provide the details of the proof on the existence of Bogdanov-Takens ...