@article{ZakharovaVadivasovaAnishchenkoetal.2010, author = {Zakharova, Anna and Vadivasova, Tatjana and Anishchenko, Vadim S. and Koseska, Aneta and Kurths, J{\"u}rgen}, title = {Stochastic bifurcations and coherencelike resonance in a self-sustained bistable noisy oscillator}, issn = {1539-3755}, doi = {10.1103/Physreve.81.011106}, year = {2010}, abstract = {We investigate the influence of additive Gaussian white noise on two different bistable self-sustained oscillators: Duffing-Van der Pol oscillator with hard excitation and a model of a synthetic genetic oscillator. In the deterministic case, both oscillators are characterized with a coexistence of a stable limit cycle and a stable equilibrium state. We find that under the influence of noise, their dynamics can be well characterized through the concept of stochastic bifurcation, consisting in a qualitative change of the stationary amplitude distribution. For the Duffing-Van der Pol oscillator analytical results, obtained for a quasiharmonic approach, are compared with the result of direct computer simulations. In particular, we show that the dynamics is different for isochronous and anisochronous systems. Moreover, we find that the increase of noise intensity in the isochronous regime leads to a narrowing of the spectral line. This effect is similar to coherence resonance. However, in the case of anisochronous systems, this effect breaks down and a new phenomenon, anisochronous-based stochastic bifurcation occurs.}, language = {en} } @article{ZakharovaKurthsVadivasovaetal.2011, author = {Zakharova, Anna and Kurths, J{\"u}rgen and Vadivasova, Tatyana and Koseska, Aneta}, title = {Analysing dynamical behavior of cellular networks via stochastic bifurcations}, series = {PLoS one}, volume = {6}, journal = {PLoS one}, number = {5}, publisher = {PLoS}, address = {San Fransisco}, issn = {1932-6203}, doi = {10.1371/journal.pone.0019696}, pages = {12}, year = {2011}, abstract = {The dynamical structure of genetic networks determines the occurrence of various biological mechanisms, such as cellular differentiation. However, the question of how cellular diversity evolves in relation to the inherent stochasticity and intercellular communication remains still to be understood. Here, we define a concept of stochastic bifurcations suitable to investigate the dynamical structure of genetic networks, and show that under stochastic influence, the expression of given proteins of interest is defined via the probability distribution of the phase variable, representing one of the genes constituting the system. Moreover, we show that under changing stochastic conditions, the probabilities of expressing certain concentration values are different, leading to different functionality of the cells, and thus to differentiation of the cells in the various types.}, language = {en} }