Logistic map driven by dichotomous noise

Logistic map analysis of biomolecular network evolution

We study the expansion of biomolecular networks from the view point of first evolutionary principles based on the duplication and divergence of ancestral genes. The expansion of gene families and subnetworks is analyzed in terms of logistic map compositions, which capture the varying functional constraints of individual genes in the course of evolution. Using a mean-field approach, we then demonstrate the existence of spontaneous growth-rate variations between gene families and discuss the relevance of such heterogeneous expansions for the emergent properties of actual biomolecular networks.

Effect of parametric dichotomous Markov noise on the properties of crises in dynamical systems

Properties of dynamical systems with dichotomous Markov noise which exhibit crises are investigated. We find numerically the dependence of the mean residence time on the precrisis attractor on the transition rate (or transition probability in the discrete-time case) of dichotomous Markov noise. To explain this dependence, we construct a simple Markov chain model, which allows us to find the mean residence time for the given transition rate with a good accuracy. Next, we find the distribution of residence times for a system driven by dichotomous Markov noise and also build a simple model to explain its properties.

Quantum escape kinetics over a fluctuating barrier

The escape rate of a particle over a fluctuating barrier in a double-well potential exhibits resonance at an optimum value of correlation time of fluctuation. This has been shown to be important in several variants of kinetic model of chemical reactions. We extend the analysis of this phenomenon of resonant activation to quantum domain to show how quantization significantly enhances resonant activation at low temperature due to tunneling.