44 research outputs found
Bistable Traveling Waves for Monotone Semiflows with Applications
This paper is devoted to the study of traveling waves for monotone evolution
systems of bistable type. Under an abstract setting, we establish the existence
of bistable traveling waves for discrete and continuous-time monotone
semiflows. This result is then extended to the cases of periodic habitat and
weak compactness, respectively. We also apply the developed theory to four
classes of evolution systems
Traveling waves and spreading speeds for time-space periodic monotone systems
The theory of traveling waves and spreading speeds is developed for
time-space periodic monotone semiflows with monostable structure. By using
traveling waves of the associated Poincar\'e maps in a strong sense, we
establish the existence of time-space periodic traveling waves and spreading
speeds. We then apply these abstract results to a two species competition
reaction-advection-diffusion model. It turns out that the minimal wave speed
exists and coincides with the single spreading speed for such a system no
matter whether the spreading speed is linearly determinate. We also obtain a
set of sufficient conditions for the spreading speed to be linearly
determinate.Comment: arXiv admin note: text overlap with arXiv:1410.459
Propagation Phenomena for A Reaction-Advection-Diffusion Competition Model in A Periodic Habitat
This paper is devoted to the study of propagation phenomena for a
Lotka-Volterra reaction-advection-diffusion competition model in a periodic
habitat. We first investigate the global attractivity of a semi-trival steady
state for the periodic initial value problem. Then we establish the existence
of the rightward spreading speed and its coincidence with the minimal wave
speed for spatially periodic rightward traveling waves. We also obtain a set of
sufficient conditions for the rightward spreading speed to be linearly
determinate. Finally, we apply the obtained results to a prototypical
reaction-diffusion model
seasonal influence on age-structured invasive species with yearly generation
How do seasonal successions influence the propagation dynamics of an
age-structured invasive species? We investigate this problem by considering the
scenario that the offsprings are reproduced in spring and then reach maturation
in fall within the same year. For this purpose, a reaction-diffusion system is
proposed, with yearly periodic time delay and spatially nonlocal response
caused by the periodic developmental process. By appealing to the recently
developed dynamical system theories, we obtain the invasion speed and its
coincidence with the minimal speed of time periodic traveling waves. The
characterizations of suggest that (i) time delay decreases the speed and
its periodicity may further do so; (ii) the optimal time to slow down the
invasion is the season without juveniles; (iii) the speed increases to infinity
with the same order as the square root of the diffusion rate
Notes on nonlocal dispersal equations in a periodic habitat
In this paper, we prove that the solution maps of a large class of nonlocal
dispersal equations are -contractions, where is the Kuratowski
measure of noncompactness. Then we give some remarks on the spreading speeds
and traveling waves for such evolution equations in a periodic habitat
Competition in periodic media: I -- Existence of pulsating fronts
This paper is concerned with the existence of pulsating front solutions in
space-periodic media for a bistable two-species competition--diffusion
Lotka--Volterra system. Considering highly competitive systems, a simple "high
frequency or small amplitudes" algebraic sufficient condition for the existence
of pulsating fronts is stated. This condition is in fact sufficient to
guarantee that all periodic coexistence states vanish and become unstable as
the competition becomes large enough
Analysis of Spreading Speeds with an Application to Cellular Neural Networks
In this paper, we focus on some properties of the spreading speeds which can
be estimated by linear operators approach, such as the sign, the continuity and
a limiting case which admits no spreading phenomenon. These theoretical results
are well applied to study the effect of templates on propagation speeds for
cellular neural networks (CNNs), which admit three kinds of propagating
phenomenon.Comment: 19 pages, 9 figure
Asymptotic convergence to pushed wavefronts in a monostable equation with delayed reaction
We study the asymptotic behaviour of solutions to the delayed monostable
equation : with monotone reaction term . Our basic assumption is that
this equation possesses pushed traveling fronts. First we prove that the pushed
wavefronts are nonlinearly stable with asymptotic phase. Moreover, combinations
of these waves attract, uniformly on , every solution of equation with
the initial datum sufficiently rapidly decaying at one (or at the both)
infinities of the real line. These results provide a sharp form of the theory
of spreading speeds for equation .Comment: 27 pages, 1 figure, submitte
Propagation Dynamics for Monotone Evolution Systems without Spatial Translation Invariance
In this paper,under an abstract setting we establish the existence of
spatially inhomogeneous steady states and the asymptotic propagation properties
for a large class of monotone evolution systems without spatial translation
invariance. Then we apply the developed theory to study traveling waves and
spatio-temporal propagation patterns for time-delayed nonlocal equations,
reaction-diffusion equations in a cylinder, and asymptotically homogeneous
KPP-type equations. We also obtain the existence of steady state solutions and
asymptotic spreading properties of solutions for a time-delayed
reaction-diffusion equation subject to the Dirichlet boundary condition
Propagation Dynamics for a Spatially Periodic Integrodifference Competition Model
In this paper, we study the propagation dynamics for a class of
integrodifference competition models in a periodic habitat. An interesting
feature of such a system is that multiple spreading speeds can be observed,
which biologically means different species may have different spreading speeds.
We show that the model system admits a single spreading speed, and it coincides
with the minimal wave speed of the spatially periodic traveling waves. A set of
sufficient conditions for linear determinacy of the spreading speed is also
given.Comment: arXiv admin note: text overlap with arXiv:1410.4591, arXiv:1504.0378