Biomedical subjects

Steffen Trimper

Publications and source records attributed to Steffen Trimper.

5 recordsLinked to original sources

PubMed2003

Weighted scale-free networks with stochastic weight assignments.

We propose a model of weighted scale-free networks incorporating a stochastic scheme for weight assignments to the links, taking into account both the popularity and fitness of a node. As the network grows, the weights of links are driven either by the connectivity with probability p or by the fitness with probability 1-p. Numerical results show that the total weight exhibits a power-law distribution with an exponent sigma that depends on the probability p. The exponent sigma decreases continuously as p increases. For p=0, the scaling behavior is the same as that of the connectivity distribution. An analytical expression for the total weight is derived so as to explain the features observed in the numerical results. Numerical results are also presented for a generalized model with a fitness-dependent link formation mechanism.

Journal Article↗

PubMed2002

Random walks with feedback on fractal lattices.

We study numerically a random walk under the competitive processes of a self-organized feedback coupling, characterized by a strength lambda and an underlying fractal lattice. Whereas a fractal structure favors a subdiffusive behavior, a dynamical feedback leads either to localization in case of an attractive feedback, lambda>0, or to superdiffusion for a repulsive memory strength lambda<0. Under the influence of both processes the dynamical exponent z is changed. For a Sierpinski gasket or a Sierpinski carpet with repulsive feedback coupling we get 2/z=1.04 or 2/z=1.08, respectively. When an attractive feedback is dominant, the system offers localization as in the case of a random walk in regular lattices. The numerical results are strongly supported by analytical studies based on scaling arguments.

Journal Article↗

PubMed2002

Memory driven Ginzburg-Landau model.

The time evolution of a bistable Ginzburg-Landau model (GL) with a non-Markovian memory term of strength lambda is studied. Due to the nonlinear feedback coupling, the two branches of the stationary solution are not only controlled by the sign of the initial condition P(0), but also by the strength and the sign of lambda. Whereas in case of a positive lambda the stationary solution is ever reduced through the memory, it may be increasing for lambda<0. In that case the system is also able to switch over between both branches of the stationary solution. Such an ability is exclusively achieved for a negative lambda within an interval -u<lambda<lambda(c), where lambda(c) is a critical memory strength and u is the strength of the conventional nonlinear term within the GL. The complete phase diagram is presented in the P(0)-lambda plane analytically and numerically.

Journal Article↗

PubMed2002

Evolution model with a cumulative feedback coupling.

The paper is concerned with a toy model that generalizes the standard Lotka-Volterra equation for a certain population by introducing a competition between instantaneous and accumulative, history-dependent nonlinear feedback the origin of which could be a contribution from any kind of mismanagement in the past. The results depend on the sign of that additional cumulative loss or gain term of strength lambda. In case of a positive coupling the system offers a maximum gain achieved after a finite time but the population will die out in the long time limit. In this case the instantaneous loss term of strength u is irrelevant and the model exhibits an exact solution. In the opposite case lambda<0 the time evolution of the system is terminated in a crash after t(s) provided u=0. This singularity after a finite time can be avoided if u not equal to 0. The approach may well be of relevance for the qualitative understanding of more realistic descriptions.

Journal Article↗

PubMed2002

Classical kinetical Bose gas.

An autocatalytic reaction combined with spontaneous creation and annihilation processes of particles are studied in a quantum formalism of the master equation in a lattice gas representation with unrestricted occupancy. In case the system is activated by a linear coupling to a heat bath the problem can be solved exactly and the stationary particle density follows the Bose distribution. The relation to spin-flip processes with a restricted occupancy is discussed. Different from those processes the relaxation time and the density fluctuation increase in the high-temperature limit. On a small scale the mutual interaction between the particles is relevant. While in case of a repulsive interaction the stationary solution becomes unstable against short wavelength fluctuations, an attractive interaction leads to an instability for long wavelength fluctuations. The system decays in domains, the size of which can be estimated as a function of temperature and interaction strength. The model is also appropriate to study the growth of open bacterial colonies under the influence of a competitive interaction between the species.

Journal Article↗