The nonlinear dynamics of cardiac action potentials is explained via simple model equations describing the membrane potential and the inward and outward currents through the membrane. The equations approximate ionic models, yet are expressed as polynomial functions, and robustly capture the phase-space dynamics of action potentials.

An iterative method is given for computing the polynomials that vanish on the basin of attraction of a steady state in discrete polynomial dynamics with finite field coefficients. The algorithm is applied to dynamics of a T cell survival network where it is used to compare transition maps conditional on a basin of attraction.

Complex dynamics deals with the iteration of holomorphic functions. As is well known, the first functions to be studied which gave non-trivial dynamics were quadratic polynomials, which produced beautiful computer generated pictures of Julia sets and the Mandelbrot set. In the same spirit, this article aims to study the dynamics of the simplest non-trivial quasiregular mappings. These are mappi...

This paper is concerned with the reachability computation problem for polynomial dynamical systems. Such computations constitute a crucial component in algorithmic verification tools for hybrid systems and embedded software with polynomial dynamics, which have found applications in many engineering domains. We describe two methods for overapproximating reachable sets of such systems; these meth...

Very little is currently known about the dynamics of non-polynomial entire maps in several complex variables. The family transcendental H\'enon offers potential combining ideas from one variable, and polynomial two. Here we show that these all have infinite topological measure theoretic entropy. proof also implies existence infinitely many periodic orbits any order greater than

The use of short order polynomial approximations to 1/x as a UV filter for HMC is investigated. Previous work in the Schwinger model (2D QED) showed that the integration step size may be increased within a multiple time scale integration by separating the UV and IR dynamics with a polynomial filter. We test the same method within the framework of Lattice QCD. c Copyright owned by the author(s) ...

‎This paper obtains the exact solutions of the wave equation as a second-order partial differential equation (PDE)‎. ‎We are going to calculate polynomial and non-polynomial exact solutions by using Lie point symmetry‎. ‎We demonstrate the generation of such polynomial through the medium of the group theoretical properties of the equation‎. ‎A generalized procedure for polynomial solution is pr...

abstract. suppose g is an nvertex and medge simple graph with edge set e(g). an integervalued function f: e(g) → z is called a flow. tutte was introduced the flow polynomial f(g, λ) as a polynomial in an indeterminate λ with integer coefficients by f(g,λ) in this paper the flow polynomial of some dendrimers are computed.

This paper uses the reliability polynomial, introduced by Moore and Shannon in 1956, to analyze the effect of network structure on diffusive dynamics such as the spread of infectious disease. We exhibit a representation for the reliability polynomial in terms of what we call structural motifs that is well suited for reasoning about the effect of a network's structural properties on diffusion ac...

Stability and performance of a system can be inferred from the evolution of statistical characteristic (i.e. mean, variance...) of system states. The polynomial chaos of Wiener provides a computationally effective framework for uncertainty quantification of stochastic dynamics in terms of statistical characteristic. In this work, polynomial chaos is used for uncertainty quantification of fracti...