43, Baltiyskaya Street, Vladivostok, 690041, Russia
V.I. Il'ichev Pacific Oceanological Institute of the Far-Eastern Branch of RAS
Kon'kov L. E., Chizhova T. L., Koudryashova Y. V., Chodnovsky V. M., Prants S. V.
Nonlinear dynamics of a cellular Ryanodine channel
2008, Vol. 4, No. 2, pp. 181-192
Dynamics of calcium ions releasing is studied in the framework of a simple electron-conformal model of a cellular Ryanodine channel, a giant protein molecule playing an important role in many biochemical processes. Taking into account only two coupled degrees of freedom (external conformal and internal electron ones), we introduce a Hamiltonian of a cellular Ryanodine channel belonging to the class of spin-boson Hamiltonians. The corresponding equations of motion constitute a nonlinear five-dimensional dynamical system with two isolated integrals of motion. Hamiltonian chaos may arise in that system as a result of a transversal intersection of stable and unstable manifolds of an unperturbed separatrix. The maximal Lyapunov exponent computed is positive in a certain range of values of control parameters. Poincare sections computed demonstrate typical patterns of Hamiltonian chaos with coexisting domains of regular and chaotic motion corresponding to regular and chaotic oscillations of the internal state of the cellular Ryanodine channel. An intermittency of those oscillations is found numerically and explained in terms of a stickiness effect of trajectories to the boundaries of stability islands in the phase space. Thus, even a single cellular Ryanodine channel is able to work in different regimes (regular, chaotic and weakly chaotic) depending on the values of the control parameters.
Budyansky M. V., Prants S. V., Uleysky M.
Chaotic advection in a meandering jet flow
2006, Vol. 2, No. 2, pp. 165-180
The paper studies the transport, mixing and chaotic advection of passive scalars in a meandering jet flow with a periodic perturbation. The stability of the critical points has been performed. We have found all topologically different regimes of the flow along with their bifurcations. It is shown that the process of mixing of passive scalars exhibits fractal-like patterns. There are some geometric regularities in the relationship between 1) the initial coordinates of scalars and 2) the number of rotations of particles around elliptic points and their escape time from a particular domain in the phase-space. It is shown how these regularities manifest in the evolution of a material line. The results obtained may be used in modelling Lagrangian transport and mixing of water masses with different characteristics in meandering western boundary currents such as the Kuroshio and the Gulf Stream.