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

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.

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 Pancake Collapse and Structure Formation from CDM Density Fluctuations

1999 ◽  
Vol 183 ◽  
pp. 250-250
Author(s):  
T. Hosokawa ◽  
M. Yokosawa
Keyword(s):  
Dark Matter ◽  
Mass Fraction ◽  
Cold Dark Matter ◽  
High Accuracy ◽  
Density Fluctuations ◽  
Radiative Cooling ◽  
Shock Formation ◽  
De Sitter ◽  
One Dimensional ◽  
De Sitter Universe

Several scales' density fluctuations which exist in the early universe will first gravitationally collapse along one axis and make pancake-like structures. If the collapsed baryonic pancake heats up over 104K by shock formation, radiative cooling begins to work and mass accretion toward the central region will advance. Because of this effect, mass fraction of the high density layer becomes large. Densities and widths of the layers will reflect masses of structures (e.g. galaxy) which will be formed after caustics. In this respect, we assumed an Einstein-de Sitter universe dominated by cold dark matter (ΩDM = 0.9) and investigated the evolutions of fluctuations numerically using one-dimensional hydrodynamic plus N-body codes. We applied a new method for larger fluctuation scales; it is a hybrid method of Eulerian PPM and Zeldovich approximation and it can simulate around the central pancake region with high accuracy.

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