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Full-Text Articles in Physical Sciences and Mathematics
A Kuramoto Model Approach To Predicting Chaotic Systems With Echo State Networks, Sophie Wu, Jackson Howe
A Kuramoto Model Approach To Predicting Chaotic Systems With Echo State Networks, Sophie Wu, Jackson Howe
Undergraduate Student Research Internships Conference
An Echo State Network (ESN) with an activation function based on the Kuramoto model (Kuramoto ESN) is implemented, which can successfully predict the logistic map for a non-trivial number of time steps. The reservoir in the prediction stage exhibits binary dynamics when a good prediction is made, but the oscillators in the reservoir display a larger variability in states as the ESN’s prediction becomes worse. Analytical approaches to quantify how the Kuramoto ESN’s dynamics relate to its prediction are explored, as well as how the dynamics of the Kuramoto ESN relate to another widely studied physical model, the Ising model.
Travelling Wave Solutions On A Cylindrical Geometry, Karnav R. Raval
Travelling Wave Solutions On A Cylindrical Geometry, Karnav R. Raval
Undergraduate Student Research Internships Conference
Fluid equations are generally quite difficult and computationally-expensive to solve. However, if one is primarily interested in how the surface of the fluid deforms, we can re-formulate the governing equations purely in terms of free surface variables. Reformulating equations in such a way drastically cuts down on computational cost, and may be useful in areas such as modelling blood flow. Here, we study one such free-boundary formulation on a cylindrical geometry.
Using An Analytical Approach Of The Kuramoto Model To Stimulate 3d Neural Activity Of The Stomach, Morteza Al Rabya
Using An Analytical Approach Of The Kuramoto Model To Stimulate 3d Neural Activity Of The Stomach, Morteza Al Rabya
Undergraduate Student Research Internships Conference
No abstract provided.
Modelling Non-Linear Functional Responses In Competitive Biological Systems., Nickolas Goncharenko
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 …
Real Solution Of Dae And Pdae System, Zahra Mohammadi, Greg Reid
Real Solution Of Dae And Pdae System, Zahra Mohammadi, Greg Reid
Western Research Forum
General systems of differential equations don't have restrictions on the number or type of equations. For example, they can be over or under-determined, and also contain algebraic constraints (e.g. algebraic equations such as in Differential-Algebraic equations (DAE) and Partial differential algebraic equations (PDAE). Increasingly such general systems arise from mathematical modeling of engineering and science problems such as in multibody mechanics, electrical circuit design, optimal control, chemical kinetics and chemical control systems. In most applications, only real solutions are of interest, rather than complex-valued solutions. Much progress has been made in exact differential elimination methods, which enable characterization of all …
P26. Global Exponential Stabilization On So(3), Soulaimane Berkane
P26. Global Exponential Stabilization On So(3), Soulaimane Berkane
Western Research Forum
Global Exponential Stabilization on SO(3)