arXiv subjects

T. Martinetz

Publications and source records attributed to T. Martinetz.

4 recordsLinked to original sources

arXiv1998

How fast do structures emerge in hypercycle-systems?

A general framework for the simulation of reaction-diffusion systems with probabilistic cellular automata is presented. The basic reaction probabilities of the chemical model translate directly into the transition rules of the automaton, thus allowing a clear comparison between simulation results and analytic calculations. This framework is then applied to simulations of hypercycle-systems in up to three dimensions. Furthermore, a new measurement quantity is introduced and applied to the hypercycle-systems in two and three dimensions. It can be shown that this quantity can be interpreted as a measure for the macroscopic order of the hypercycle systems.

adap-org↗

arXiv1998

Aftershocks in Coherent-Noise Models

The decay pattern of aftershocks in the so-called 'coherent-noise' models [M. E. J. Newman and K. Sneppen, Phys. Rev. E54, 6226 (1996)] is studied in detail. Analytical and numerical results show that the probability to find a large event at time $t$ after an initial major event decreases as $t^{-τ}$ for small $t$, with the exponent $τ$ ranging from 0 to values well above 1. This is in contrast to Sneppen und Newman, who stated that the exponent is about 1, independent of the microscopic details of the simulation. Numerical simulations of an extended model [C. Wilke, T. Martinetz, Phys. Rev. E56, 7128 (1997)] show that the power-law is only a generic feature of the original dynamics and does not necessarily appear in a more general context. Finally, the implications of the results to the modeling of earthquakes are discussed.

physics.data-an↗

arXiv1998

Large-scale evolution and extinction in a hierarchically structured environment

A class of models for large-scale evolution and mass extinctions is presented. These models incorporate environmental changes on all scales, from influences on a single species to global effects. This is a step towards a unified picture of mass extinctions, which enables one to study coevolutionary effects and external abiotic influences with the same means. The generic features of such models are studied in a simple version, in which all environmental changes are generated at random and without feedback from other parts of the system.

adap-org↗

arXiv1997

A Simple Model of Evolution with Variable System Size

A simple model of biological extinction with variable system size is presented that exhibits a power-law distribution of extinction event sizes. The model is a generalization of a model recently introduced by Newman (Proc. R. Soc. Lond. B265, 1605 (1996). Both analytical and numerical analysis show that the exponent of the power-law distribution depends only marginally on the growth rate $g$ at which new species enter the system and is equal to the one of the original model in the limit $g\to\infty$. A critical growth rate $g_c$ can be found below which the system dies out. Under these model assumptions stable ecosystems can only exist if the regrowth of species is sufficiently fast.

physics.bio-ph↗