scholarly journals Asymptotic dynamics for the small data weakly dispersive one-dimensional Hamiltonian ABCD system

2019 ◽  
Vol 373 (2) ◽  
pp. 1043-1107
Author(s):  
Chulkwang Kwak ◽  
Claudio Muñoz
Keyword(s):  
Small Data ◽  
One Dimensional ◽  
Asymptotic Dynamics

scholarly journals A one dimensional analogue of the vorticity equation

1997 ◽  
Vol 56 (1) ◽  
pp. 119-134
Author(s):  
K. Sriskandarajah
Keyword(s):  
Soliton Solutions ◽  
Vorticity Equation ◽  
Advection Equation ◽  
Small Data ◽  
Qualitative Properties ◽  
One Dimensional ◽  
Perturbation Problem ◽  
Order Hyperbolic Equation ◽  
The One ◽  
Second Order Hyperbolic Equation

We study the qualitative properties of the one dimensional analogue of the Helmholtz vorticity advection equation. The second order hyperbolic equation has the unusual characteristic of disturbances propagating at infinite speed. The global solution for Goursat data is given in closed form. We also obtain qualitative results on the nodal curve where the solution is zero. A related perturbation problem is considered and solutions for small data are obtained. The forced vorticity equation admits a class of soliton solutions.

POPULATION DYNAMICS IN HETEROGENEOUS ENVIRONMENTS: A DISCRETE MODEL

2000 ◽  
Vol 10 (08) ◽  
pp. 1993-2000 ◽  
Author(s):  
BASTIEN FERNANDEZ ◽  
VALERY TERESHKO
Keyword(s):  
Population Dynamics ◽  
Periodic Orbit ◽  
Discrete Model ◽  
Mean Field ◽  
Heterogeneous Environments ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Population Spread ◽  
Asymptotic Dynamics ◽  
Time Periodic

We study the dynamics of a multidimensional coordinate-dependent mapping governing the time evolution of a population spread over a one-dimensional lattice. The nonlinearity is of mean-field type and the dependence on coordinates, given by the so-called fitness, allows to take into account the spatial heterogeneities of the habitat. A global picture of the dynamics is given in the case without diffusion and in the case with diffusion when the fitness is homogeneous and leads to a periodic orbit. Moreover it is shown that, periodic fitnesses close to homogeneous ones impose their periodicity on the asymptotic dynamics when the latter is time-periodic.

Cellular Automata Communication Models

2010 ◽  
Vol 1 (3) ◽  
pp. 66-84 ◽  
Author(s):  
Predrag T. Tošic
Keyword(s):  
Distributed Computing ◽  
Cellular Automata ◽  
Large Scale ◽  
Relevant Model ◽  
One Dimensional ◽  
Threshold Functions ◽  
Communication Models ◽  
Ca Model ◽  
Asymptotic Dynamics ◽  
Update Rules

In this paper, cellular automata (CA) are viewed as an abstract model for distributed computing. The author argues that the classical CA model must be modified in several important respects to become a relevant model for large-scale MAS. The paper first proposes sequential cellular automata (SCA) and formalizes deterministic and nondeterministic versions of SCA. The author then analyzes differences in possible dynamics between classical parallel CA and various SCA models. The analysis in this paper focuses on one-dimensional parallel and sequential CA with node update rules restricted to simple threshold functions, as arguably the simplest totalistic, yet non-linear (and non-affine) update rules. The author identifies properties of asymptotic dynamics that can be proven to be entirely due to the assumption of perfect synchrony in classical, parallel CA. Finally, the paper discusses what an appropriate CA-based abstraction would be for large-scale distributed computing, insofar as the inter-agent communication models. In that context, the author proposes genuinely asynchronous CA and discusses main differences between genuinely asynchronous CA and various weakly asynchronous sequential CA models found in the literature.

scholarly journals ASYMPTOTIC DYNAMICS OF A CLASS OF COUPLED OSCILLATORS DRIVEN BY WHITE NOISES

2013 ◽  
Vol 13 (04) ◽  
pp. 1350002 ◽  
Author(s):  
WENXIAN SHEN ◽  
ZHONGWEI SHEN ◽  
SHENGFAN ZHOU
Keyword(s):  
Coupled Oscillators ◽  
Practical Importance ◽  
Second Order ◽  
Random Attractor ◽  
Coupling Coefficients ◽  
Horizontal Curve ◽  
Frequency Locking ◽  
One Dimensional ◽  
Asymptotic Dynamics ◽  
White Noises

This paper is devoted to the study of the asymptotic dynamics of a class of coupled second order oscillators driven by white noises. It is shown that any system of such coupled oscillators with positive damping and coupling coefficients possesses a global random attractor. Moreover, when the damping and the coupling coefficients are sufficiently large, the global random attractor is a one-dimensional random horizontal curve regardless of the strength of the noises, and the system has a rotation number, which implies that the oscillators in the system tend to oscillate with the same frequency eventually and therefore the so-called frequency locking is successful. The results obtained in this paper generalize many existing results on the asymptotic dynamics for a single second order noisy oscillator to systems of coupled second order noisy oscillators. They show that coupled damped second order oscillators with large damping have similar asymptotic dynamics as the limiting coupled first order oscillators as the damping goes to infinite and also that coupled damped second order oscillators have similar asymptotic dynamics as their proper space continuous counterparts, which are of great practical importance.

scholarly journals One-dimensional fuzzy dark matter models: Structure growth and asymptotic dynamics

2021 ◽  
Vol 103 (8) ◽  
Author(s):  
Tim Zimmermann ◽  
Nico Schwersenz ◽  
Massimo Pietroni ◽  
Sandro Wimberger
Keyword(s):  
Dark Matter ◽  
One Dimensional ◽  
Asymptotic Dynamics

Glider Collisions in Hybrid Cellular Automaton with Memory Rule (43,74)

2017 ◽  
Vol 27 (06) ◽  
pp. 1750082 ◽  
Author(s):  
Bo Chen ◽  
Fangyue Chen ◽  
Genaro J. Martínez
Keyword(s):  
Vector Space ◽  
Cellular Automaton ◽  
Analytical Method ◽  
Quantitative Approach ◽  
One Dimensional ◽  
Hybrid Mechanism ◽  
Wide Range ◽  
Asymptotic Dynamics ◽  
Definition Of ◽  
With Memory

In the case of one-dimensional cellular automaton (CA), a hybrid CA (HCA) is the member whose evolution of the cells is dependent on nonunique global functions. The HCAs exhibit a wide range of traveling and stationary localizations in their evolution. We focus on HCA with memory (HCAM) because they produce a host of gliders and complicated glider collisions by introducing the hybrid mechanism. In particular, we undertake an exhaustive search of gliders and describe their collisions using quantitative approach in HCAM[Formula: see text]. By introducing the symbol vector space and exploiting the mathematical definition of HCAM, we present an analytical method of complex asymptotic dynamics of the gliders.

scholarly journals On the Asymptotic Behavior of Solutions to the Vlasov–Poisson System

2021 ◽  
Author(s):  
Alexandru D Ionescu ◽  
Benoit Pausader ◽  
Xuecheng Wang ◽  
Klaus Widmayer
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Behavior Of Solutions ◽  
Small Data ◽  
Poisson System ◽  
Dispersive Analysis ◽  
Asymptotic Dynamics

Abstract We prove small data modified scattering for the Vlasov–Poisson system in dimension $d=3$, using a method inspired from dispersive analysis. In particular, we identify a simple asymptotic dynamics related to the scattering mass.

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