2,177 research outputs found
Existence and Stability of Positive Periodic Solutions for a Neutral Multispecies Logarithmic Population Model with Feedback Control and Impulse
We investigate a neutral multispecies logarithmic population model with feedback control and impulse. By applying the contraction mapping principle and some inequality techniques, a set of easily applicable criteria for the existence, uniqueness, and global attractivity of positive periodic solution are established. The conditions we obtained are weaker than the previously known ones and can be easily reduced to several special cases. We also give an example to illustrate the applicability of our results
Traveling waves and Compactons in Phase Oscillator Lattices
We study waves in a chain of dispersively coupled phase oscillators. Two
approaches -- a quasi-continuous approximation and an iterative numerical
solution of the lattice equation -- allow us to characterize different types of
traveling waves: compactons, kovatons, solitary waves with exponential tails as
well as a novel type of semi-compact waves that are compact from one side.
Stability of these waves is studied using numerical simulations of the initial
value problem.Comment: 22 pages, 25 figure
Energy-transport systems for optical lattices: derivation, analysis, simulation
Energy-transport equations for the transport of fermions in optical lattices
are formally derived from a Boltzmann transport equation with a periodic
lattice potential in the diffusive limit. The limit model possesses a formal
gradient-flow structure like in the case of the energy-transport equations for
semiconductors. At the zeroth-order high temperature limit, the
energy-transport equations reduce to the whole-space logarithmic diffusion
equation which has some unphysical properties. Therefore, the first-order
expansion is derived and analyzed. The existence of weak solutions to the
time-discretized system for the particle and energy densities with periodic
boundary conditions is proved. The difficulties are the nonstandard degeneracy
and the quadratic gradient term. The main tool of the proof is a result on the
strong convergence of the gradients of the approximate solutions. Numerical
simulations in one space dimension show that the particle density converges to
a constant steady state if the initial energy density is sufficiently large,
otherwise the particle density converges to a nonconstant steady state
Clustering in Cell Cycle Dynamics with General Response/Signaling Feedback
Motivated by experimental and theoretical work on autonomous oscillations in
yeast, we analyze ordinary differential equations models of large populations
of cells with cell-cycle dependent feedback. We assume a particular type of
feedback that we call Responsive/Signaling (RS), but do not specify a
functional form of the feedback. We study the dynamics and emergent behaviour
of solutions, particularly temporal clustering and stability of clustered
solutions. We establish the existence of certain periodic clustered solutions
as well as "uniform" solutions and add to the evidence that cell-cycle
dependent feedback robustly leads to cell-cycle clustering. We highlight the
fundamental differences in dynamics between systems with negative and positive
feedback. For positive feedback systems the most important mechanism seems to
be the stability of individual isolated clusters. On the other hand we find
that in negative feedback systems, clusters must interact with each other to
reinforce coherence. We conclude from various details of the mathematical
analysis that negative feedback is most consistent with observations in yeast
experiments.Comment: To appear in J. Theoretical Biology 292 (2012), 103-11
- …