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Analysis of a Non-linear Partial Difference Equation, and Its Application to Cardiac Dynamics
Partial difference equation Non-linear Cardiac dynamics Singular perturbation method Spatial bifurcations
2015/8/27
A model of a strip of cardiac tissue consisting of a one-dimensional chain of cardiac units is derived in the form of a non-linear partial difference equation. Perturbation analysis is performed on th...
Dynamics of a model of two delay-coupled relaxation oscillators
Coupled oscillators Devil’s Staircase Delay-differential equations
2015/8/27
This paper investigates the dynamics of a new model of two coupled relaxation oscilla-tors. The model replaces the usual DDE (differential-delay equation) formulation with a discrete-time approach wit...
Hopf Bifurcations in Two-Player Delayed Replicator Dynamics
Hopf Bifurcations Two-Player Delayed Replicator Dynamics
2015/8/26
We investigate the dynamics of two-strategy replicator equa-tions in which competition between strategies is delayed by a given time interval T. Taking T as a bifurcation parameter, we demonstrate the...
Hopf Bifurcations in Delayed Rock–Paper–Scissors Replicator Dynamics
Replicator Delay Hopf bifurcation Limit cycle Lindstedt
2015/8/26
We investigate the dynamics of three-strategy (rock–paper–scissors) replicator equations in which the fitness of each strategy is a function of the population frequencies delayed by a time interval T....
Human infants actively forage for visual information from the moment of birth onward. Although we know a great deal about
how stimulus characteristics influence looking behavior in the first few post...
This paper is an informal discussion of how geometry and numerical analysis
are intertwined in the computational study of dynamical systems and their bifurcations.
We use the example of determining ...
Nonlinear Dynamics and Chaos: Where do we go from here?
Dynamics and Chaos Colston conference
2015/8/25
In keeping with the spirit of the Colston conference on Nonlinear Dynam-
ics and Chaos, this chapter emphasizes ideas more than details, describing
my vision of how the bifurcation theory of multipl...
Majority dynamics on trees and the dynamic cavity method
Voters independent distribution random variables the initialization
2015/8/20
An elector sits on each vertex of an in nite tree of degree k, and has to decide between two alternatives.At each time step, each elector switches to the opinion of the majority of her neighbors. We a...
Parameter set estimation of systems with uncertain nonparametric dynamics and disturbances
Parameter set the parameter estimation system dynamics parameter estimation
2015/8/12
A method is presented for parameter set estimation of open-loop stable systems with uncertain parameters and quasi-stationary disturbances. The system model is assumed to contain both parametric and n...
The Dynamics of Nucleation in Sto chastic Cahn-Morral Systems
Sto chastic Cahn-Morral Systems Nucleation
2015/4/3
Spino dal Decomp osition
Deep quenches lead to spinodal decomposition and coarsening:
• Instantaneous phase separation throughout the system.
• A fine-grained and highly interconnected ...
Hylomorphic solitons and their dynamics.
The Dynamics of Twisted Tent Maps
twisted tent map complex dynamical system dynamics fractal coded-coloring escape-time fold folding reflect filled-in Julia set twisted tent map TTM complex plane polygon
2015/1/19
This paper is a study of the dynamics of a new family of maps from the complex plane to itself, which we call twisted tent maps. A twisted tent map is a complex generalization of a real tent map. The ...
Mathematical Models of Basal Ganglia Dynamics
Basal Ganglia Bistability delayed feedback deep brain stimulation Dopaminergic neuron Parkinson's disease Tremor
2015/1/19
Physical and biological phenomena that involve oscillations on multiple time scales attract attention of mathematicians because resulting equations include a small parameter that allows for decomposin...
Existence, Stability, and Dynamics of Solitary Waves in Nonlinear Schroedinger Models with Periodic Potentials
Non-square lattices, Nonlinear waves Photonic lattices
2014/12/8
The focus of this dissertation is the existence, stability, and resulting dynamical evolution of localized stationary solutions to Nonlinear Schr¨odinger (NLS) equations with periodic confining potent...
Efficient implementation of smo othed particle hydro dynamics (SPH) with plane sweep algorithm
Smoothed particle hydrodynamics Meshfree method Neighbour search Plane sweep algorithm Morton code Segment tree Quadtree Parallelization Dam break
2014/10/10
Neighbour search (NS) is the core of any implementations of smoothed particle hydrodynamics (SPH). In this paper, we present an efficient O( N log N) neighbour search method based on the plane sweep (...