Non-linear Dynamics Commons^™

The Effect Of External Perturbations On Ecological Oscillators, Eli Goldwyn

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Analog Implementation Of The Hodgkin-Huxley Model Neuron, Zachary D. Mobille, George H. Rutherford, Jordan Brandt-Trainer, Rosangela Follmann, Epaminondas Rosa

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Analysis Of An Agent-Based Model For Integrated Pest Management With Periodic Control Strategies, Timothy Comar

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Discrete-Time Disease Model With Population Motion Under The Kolmogorov Equation View And Application, Ye Li

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Academic Skill Learning And The Problem Of Complexity I: Creational Purposeful Integrated Capability At Skill (Cpics), Martin F. Gardiner

Northeast Journal of Complex Systems (NEJCS)

Physical and mental skills are intended to achieve success at acting purposefully. As capability at any skill increases, the need to adjust details of application to complexity of context and goals will increase as well. It will become more and more important to prepare mentally for what I now term Creational Purposeful Integrated Capability at Skill (CPICS). This paper develops what I mean by CPICS. Theory concerning Complex Dynamical Systems (CDS) such as the brain and other evidence points to the likelihood that the mental operations by which our brain produces any kind of skillful behavior cannot remain constant, …

A Patterning Approach To Complexity Thinking And Understanding For Students: A Case Study, Shae L. Brown

Northeast Journal of Complex Systems (NEJCS)

Complexity thinking and understanding are vital skills for young people in these times of uncertainty and change. Such skills contribute to resilience and capacities for adaptivity and innovation. Within my teaching practice I have found students to be aware of complex dynamics, uncertainty and change, both in their lives and in the world. However, the current curriculum lacks language and process to conceptualise, articulate and develop complexity understanding. To address this problem, I developed and introduced a patterns-based design and process to a cohort of Australian secondary students. Comprising flowform patterning together with ecological metaphors, the design forms a conceptual …

Being In Uncertainties: An Inquiry-Based Model Leveraging Complexity In Teaching-Learning, Diane Rosen

Northeast Journal of Complex Systems (NEJCS)

Education is traditionally structured as a closed system, privileging result-driven methods that offer control and predictability. In recent decades this reductionist approach has been effectively challenged by interdisciplinary work in complex systems theory, revealing myriad levels of orderly disorder that make either-or, linear instruction an inadequate norm. Narrowing the broad implications of a complexity lens on education, this paper focuses on generative uncertainty in teaching-learning, a paradoxical state of epistemological and creative growth described by English poet John Keats as "the negative capability of being in uncertainties, mysteries, doubts." Opportunities to advance this potentiating capacity are especially abundant in constructivist …

Creativity As An Emergent Property Of Complex Educational System, Ceire Monahan, Mika Munakata, Ashwin Vaidya

Northeast Journal of Complex Systems (NEJCS)

The importance of creativity in education has been discussed often in the literature. While there remains no agreed-upon definition of creativity, the psychological literature points to traits of a creative person. These include the ability to think outside the box, make connections between seemingly disparate ideas, and question norms. The literature provides several examples of classroom experiments to help foster creativity in the classroom. In science and mathematics, we can start by getting students to recognize mathematics and the sciences as being creative endeavors. While these attempts are noteworthy, they are not necessarily aligned with instructional practices. In this article, …

Rethinking Educational Reforms Through A Complex Dynamical Systems Approach: Preliminary Report From An Empirical Research, Eugenia Tsiouplis, Dimitrios Stamovlasis

Northeast Journal of Complex Systems (NEJCS)

Literature on educational reforms is rich of cases where changes have been attempted, without however to attain success. Likewise the Greek education system had experienced a lot of reforms, most of which have failed to make the intended changes and they attenuated shortly after their implementation or they ceased at the stage of legislative planning. On the other hand, the traditional research have failed to develop a coherent theoretical perspective and provide satisfactory interpretations of the perpetually unsuccessful reforms. This paper is part of wider project which attempts to address the above issue following the Complex Dynamical Systems (CDS) perspective, …

Editorial Introduction To The Northeast Journal Of Complex Systems (Nejcs), Hiroki Sayama, Georgi Georgiev

Northeast Journal of Complex Systems (NEJCS)

Editorial Introduction to the Northeast Journal of Complex Systems (NEJCS)

Fractality And Power Law Distributions: Shifting Perspectives In Educational Research, Matthijs Koopmans

Northeast Journal of Complex Systems (NEJCS)

The dynamical character of education and the complexity of its constituent relationships have long been recognized, but the full appreciation of the implications of these insights for educational research is recent. Most educational research to this day tends to focus on outcomes rather than process, and rely on conventional cross-sectional designs and statistical inference methods that do not capture this complexity. This presentation focuses on two related aspects not well accommodated by conventional models, namely fractality (self-similarity, scale invariance) and power law distributions (an inverse relationship between frequency of occurrence and strength of response). Examples are presented for both phenomena …

One-Note-Samba Approach To Cosmology, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

Inspired by One Note Samba, a standard jazz repertoire, we present an outline of Bose-Einstein Condensate Cosmology. Although this approach seems awkward and a bit off the wall at first glance, it is not impossible to connect altogether BEC, Scalar Field Cosmology and Feshbach Resonance with Ermakov-Pinney equation. We also briefly discuss possible link with our previous paper which describes Newtonian Universe with Vortex in terms of Ermakov equation.

Investigation Of Fundamental Principles Of Rigid Body Impact Mechanics, Khalid Alluhydan

Mechanical Engineering Research Theses and Dissertations

In impact mechanics, the collision between two or more bodies is a common, yet a very challenging problem. Producing analytical solutions that can predict the post-collision motion of the colliding bodies require consistent modeling of the dynamics of the colliding bodies. This dissertation presents a new method for solving the two and multibody impact problems that can be used to predict the post-collision motion of the colliding bodies. Also, we solve the rigid body collision problem of planar kinematic chains with multiple contacts with external surfaces.

In the first part of this dissertation, we study planar collisions of Balls and …

The Long-Run Effects Of Tropical Cyclones On Infant Mortality, Isabel Miranda

Master's Theses

In the United States alone, each tropical cyclone causes an average of $14.6 billion worth of damages. In addition to the destruction of physical infrastructure, natural disasters also negatively impact human capital formation. These losses are often more difficult to observe, and therefore, are over looked when quantifying the true costs of natural disasters. One particular effect is an increase in infant mortality rates, an important indicator of a country’s general socioeconomic level. This paper utilizes a model created by Anttila-Hughes and Hsiang, that takes advantage of annual variation in tropical cyclones using annual spatial average maximum wind speeds and …

Characterizing The Permanence And Stationary Distribution For A Family Of Malaria Stochastic Models, Divine Wanduku

Biology and Medicine Through Mathematics Conference

No abstract provided.

School Policy Evaluated With Time-Reversible Markov Chain, Trajan Murphy, Iddo Ben-Ari

Honors Scholar Theses

In this work we propose a reversible Markov chain scheme to model for the mobility of students affected by a grade school leveling policy. This model provides unified and mathematically tractable framework in which transition functions are sampled uniformly from the set of {\bf reversible} transition functions. The results from the study appear to confirm the disadvantageous effects of this school policy, on par with the of a previous model on the same policy.

Topology And Dynamics Of Gene Regulatory Networks: A Meta-Analysis, Claus Kadelka

Biology and Medicine Through Mathematics Conference

No abstract provided.

Predicting Dynamics From Hardwiring In Canonical Low-Dimensional Coupled Networks, Anca R. Radulescu

Biology and Medicine Through Mathematics Conference

No abstract provided.

Quantifying Complex Systems Via Computational Fly Swarms, Troy Taylor

Senior Theses

Complexity is prevalent both in natural and in human-made systems, yet is not well understood quantitatively. Qualitatively, complexity describes a phenomena in which a system composed of individual pieces, each having simple interactions with one another, results in interesting bulk properties that would otherwise not exist. One example of a complex biological system is the bird flock, in particular, a starling murmuration. Starlings are known to move in the direction of their neighbors and avoid collisions with fellow starlings, but as a result of these simple movement choices, the flock as a whole tends to exhibit fluid-like movements and form …

The Effects Of Finite Precision On The Simulation Of The Double Pendulum, Rebecca Wild

Senior Honors Projects, 2010-2019

We use mathematics to study physical problems because abstracting the information allows us to better analyze what could happen given any range and combination of parameters. The problem is that for complicated systems mathematical analysis becomes extremely cumbersome. The only effective and reasonable way to study the behavior of such systems is to simulate the event on a computer. However, the fact that the set of floating-point numbers is finite and the fact that they are unevenly distributed over the real number line raises a number of concerns when trying to simulate systems with chaotic behavior. In this research we …

Mathematical Models: The Lanchester Equations And The Zombie Apocalypse, Hailey Bauer

Undergraduate Theses and Capstone Projects

This research study used mathematical models to analyze and depicted specific battle situations and the outcomes of the zombie apocalypse. The original models that predicted warfare were the Lanchester models, while the zombie apocalypse models were fictional expansions upon mathematical models used to examine infectious diseases. In this paper, I analyzed and compared different mathematical models by examining each model’s set of assumptions and the impact of the change in variables on the population classes. The purpose of this study was to understand the basics of the discrete dynamical systems and to determine the similarities between imaginary and realistic models. …

Parameter Estimation And Optimal Design Techniques To Analyze A Mathematical Model In Wound Healing, Nigar Karimli

Masters Theses & Specialist Projects

For this project, we use a modified version of a previously developed mathematical model, which describes the relationships among matrix metalloproteinases (MMPs), their tissue inhibitors (TIMPs), and extracellular matrix (ECM). Our ultimate goal is to quantify and understand differences in parameter estimates between patients in order to predict future responses and individualize treatment for each patient. By analyzing parameter confidence intervals and confidence and prediction intervals for the state variables, we develop a parameter space reduction algorithm that results in better future response predictions for each individual patient. Moreover, use of another subset selection method, namely Structured Covariance Analysis, that …

Modelling Non-Linear Functional Responses In Competitive Biological Systems., Nickolas Goncharenko

Western Research Forum

One of the most versatile and well understood models in mathematical biology is the Competitive Lotka Volterra (CLV) model, which describes the behaviour of any number of exclusively competitive species (that is each species competes directly with every other species). Despite it's success in describing many phenomenon in biology, chemistry and physics the CLV model cannot describe any non-linear environmental effects (including resource limitation and immune response of a host due to infection). The reason for this is the theory monotone dynamical systems, which was codeveloped with the CLV model, does not apply when this non-linear effect is introduced. For …

Climate Change In A Differential Equations Course: Using Bifurcation Diagrams To Explore Small Changes With Big Effects, Justin Dunmyre, Nicholas Fortune, Tianna Bogart, Chris Rasmussen, Karen Keene

CODEE Journal

The environmental phenomenon of climate change is of critical importance to today's science and global communities. Differential equations give a powerful lens onto this phenomenon, and so we should commit to discussing the mathematics of this environmental issue in differential equations courses. Doing so highlights the power of linking differential equations to environmental and social justice causes, and also brings important science to the forefront in the mathematics classroom. In this paper, we provide an extended problem, appropriate for a first course in differential equations, that uses bifurcation analysis to study climate change. Specifically, through studying hysteresis, this problem highlights …

An Inference-Driven Branch And Bound Optimization Strategy For Planning Ambulance Services, Kevin Mcdaniel

Theses, Dissertations and Capstones

Strategic placement of ambulances is important to the efficient functioning of emergency services. As part of an ongoing collaboration with Wayne County 911, we developed a strategy to optimize the placement of ambulances throughout Wayne County based on de-identified call and response data from 2016 and 2017. The primary goals of the optimization were minimizing annual operating cost and mean response time, as well as providing a constructive solution that could naturally evolve from the existing plan. This thesis details the derivation and implementation of one of the optimization strategies used in this project. It is based on parametric statistical …

Riemann-Hilbert Problem, Integrability And Reductions, Vladimir Gerdjikov, Rossen Ivanov, Aleksander Stefanov

Articles

Abstract. The present paper is dedicated to integrable models with Mikhailov reduction groups G_R ≃ D_h. Their Lax representation allows us to prove, that their solution is equivalent to solving Riemann-Hilbert problems, whose contours depend on the realization of the G_R-action on the spectral parameter. Two new examples of Nonlinear Evolution Equations (NLEE) with D_h symmetries are presented.

Practical Chaos: Using Dynamical Systems To Encrypt Audio And Visual Data, Julia Ruiter

Scripps Senior Theses

Although dynamical systems have a multitude of classical uses in physics and applied mathematics, new research in theoretical computer science shows that dynamical systems can also be used as a highly secure method of encrypting data. Properties of Lorenz and similar systems of equations yield chaotic outputs that are good at masking the underlying data both physically and mathematically. This paper aims to show how Lorenz systems may be used to encrypt text and image data, as well as provide a framework for how physical mechanisms may be built using these properties to transmit encrypted wave signals.

Surface Waves Over Currents And Uneven Bottom, Alan Compelli, Rossen Ivanov, Calin I. Martin, Michail D. Todorov

Articles

The propagation of surface water waves interacting with a current and an uneven bottom is studied. Such a situation is typical for ocean waves where the winds generate currents in the top layer of the ocean. The role of the bottom topography is taken into account since it also influences the local wave and current patterns. Specific scaling of the variables is selected which leads to approximations of Boussinesq and KdV types. The arising KdV equation with variable coefficients, dependent on the bottom topography, is studied numerically when the initial condition is in the form of the one soliton solution …

Equatorial Wave–Current Interactions, Adrian Constantin, Rossen Ivanov

Articles

We study the nonlinear equations of motion for equatorial wave–current interactions in the physically realistic setting of azimuthal two-dimensional inviscid flows with piecewise constant vorticity in a two-layer fluid with a flat bed and a free surface. We derive a Hamiltonian formulation for the nonlinear governing equations that is adequate for structure-preserving perturbations, at the linear and at the nonlinear level. Linear theory reveals some important features of the dynamics, highlighting differences between the short- and long-wave regimes. The fact that ocean energy is concentrated in the long-wave propagation modes motivates the pursuit of in-depth nonlinear analysis in the long-wave …

Neutrosophic Triplet Structures - Vol. 1, Florentin Smarandache, Memet Sahin

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory was firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs, the properties of neutrosophic sets …