54 research outputs found
Dynamics and Steady States in excitable mobile agent systems
We study the spreading of excitations in 2D systems of mobile agents where
the excitation is transmitted when a quiescent agent keeps contact with an
excited one during a non-vanishing time. We show that the steady states
strongly depend on the spatial agent dynamics. Moreover, the coupling between
exposition time () and agent-agent contact rate (CR) becomes crucial to
understand the excitation dynamics, which exhibits three regimes with CR: no
excitation for low CR, an excited regime in which the number of quiescent
agents (S) is inversely proportional to CR, and for high CR, a novel third
regime, model dependent, here S scales with an exponent , with
being the scaling exponent of with CR
Multidimensional Inverse Scattering of Integrable Lattice Equations
We present a discrete inverse scattering transform for all ABS equations
excluding Q4. The nonlinear partial difference equations presented in the ABS
hierarchy represent a comprehensive class of scalar affine-linear lattice
equations which possess the multidimensional consistency property. Due to this
property it is natural to consider these equations living in an N-dimensional
lattice, where the solutions depend on N distinct independent variables and
associated parameters. The direct scattering procedure, which is
one-dimensional, is carried out along a staircase within this multidimensional
lattice. The solutions obtained are dependent on all N lattice variables and
parameters. We further show that the soliton solutions derived from the Cauchy
matrix approach are exactly the solutions obtained from reflectionless
potentials, and we give a short discussion on inverse scattering solutions of
some previously known lattice equations, such as the lattice KdV equation.Comment: 18 page
Localization of a Breathing Crack Using Super-Harmonic Signals due to System Nonlinearity
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76712/1/AIAA-38947-457.pd
On the Floquet Theory of Delay Differential Equations
We present an analytical approach to deal with nonlinear delay differential
equations close to instabilities of time periodic reference states. To this end
we start with approximately determining such reference states by extending the
Poincar'e Lindstedt and the Shohat expansions which were originally developed
for ordinary differential equations. Then we systematically elaborate a linear
stability analysis around a time periodic reference state. This allows to
approximately calculate the Floquet eigenvalues and their corresponding
eigensolutions by using matrix valued continued fractions
Geometric Resonances in Bose-Einstein Condensates with Two- and Three-Body Interactions
We investigate geometric resonances in Bose-Einstein condensates by solving
the underlying time-dependent Gross-Pitaevskii equation for systems with two-
and three-body interactions in an axially-symmetric harmonic trap. To this end,
we use a recently developed analytical method [Phys. Rev. A 84, 013618 (2011)],
based on both a perturbative expansion and a Poincar\'e-Lindstedt analysis of a
Gaussian variational approach, as well as a detailed numerical study of a set
of ordinary differential equations for variational parameters. By changing the
anisotropy of the confining potential, we numerically observe and analytically
describe strong nonlinear effects: shifts in the frequencies and mode coupling
of collective modes, as well as resonances. Furthermore, we discuss in detail
the stability of a Bose-Einstein condensate in the presence of an attractive
two-body interaction and a repulsive three-body interaction. In particular, we
show that a small repulsive three-body interaction is able to significantly
extend the stability region of the condensate.Comment: 27 pages, 13 figure
Stability analysis and dynamics preserving nonstandard finite difference schemes for a malaria model
When both human and mosquito populations vary, forward bifurcation occurs if
the basic reproduction number R0 is less than one in the absence of disease-induced
death. When the disease-induced death rate is large enough R0 = 1 is a subcritical
backward bifurcation point. The domain for the study of the dynamics is reduced
to a compact and feasible region, where the system admits a speci c algebraic
decomposition into infective and non-infected humans and mosquitoes. Stability
results are extended and the possibility of backward bifurcation is clari ed. A
dynamically consistent nonstandard nite di erence scheme is designed.Yves Dumont was supported jointly by the French Ministry of Health and the
2007–2013 Convergence program of the European Regional Development Fund
(ERDF). Roumen Anguelov, Jean Lubuma, and Eunice Mureithi thank the South
African National Research Foundation for its support.http://www.tandfonline.com/loi/gmps20hb201
Investigation of the mathematical properties of a new negative resistance oscillator model
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