Oscillateur de Van der Pol | EPFL Graph Search

L’oscillateur de Van der Pol est un système dynamique à temps continu à un degré de liberté. Il est décrit par une coordonnée x(t) vérifiant une équation différentielle faisant intervenir deux paramètres : une pulsation propre ω et un coefficient de non-linéarité ε. Lorsque ε = 0, cet oscillateur se réduit à un oscillateur harmonique pur. Il porte le nom de Balthasar van der Pol. Histoire vignette|Ce circuit électronique à base de triode développe un régime d'oscillations forcées régies par l'équation de Van der Pol (les composants passifs sont : une résistance R, un condensateur C et un circuit couplé d'inductance L et de inductance mutuelle M) . Le circuit RLC monté en série est parcouru d'un courant i, et l'anode (ou plaque) de la triode reçoit un courant ia, tandis que la tension aux bornes de la grille de la triode est notée ug. L’oscillateur de Van der Pol est mis en régime forcé par une source de tension alternative Es. L’oscillateur de Van der Pol a

Mean-field theory revives in self-oscillatory fields with non-local coupling

A simple mean-field idea is applicable to the pattern dynamics of large assemblies of limit-cycle oscillators with non-local coupling. This is demonstrated by developing a mathematical theory for the following two specific examples of pattern dynamics. Firstly we disscuss propagation of phase waves in noisy oscillatory media, with particular concern with the existence of a critical condition for persistent propagation of the waves throughout the medium, and also with the possibility of noise-induced turbulence. Secondly, we discuss the existence of an exotic class of patterns peciliar to non-local coupling called chimera where the system is composed of two distinct domains, one coherent and the other incoherent, separated from each other with sharp boundaries.

2006

Heat wave propagation in a nonlinear chain

Francesco Piazza

We investigate the propagation of temperature perturbations in an array of coupled nonlinear oscillators at finite temperature. We evaluate the response function at equilibrium and show how the memory effects affect the diffusion properties. A comparison with nonequilibrium simulations reveals that the telegraph equation provides a reliable interpretative paradigm for describing quantitatively the propagation of a heat pulse at the macroscopic level. The results could be of help in understanding and modeling energy transport in individual nanotubes.

2009

Circadian rhythm and cell cycle

Rosamaria Cannavo

Circadian rhythms are biological processes found in most living organisms, displaying a roughly 24-hour period, responding primarily to light darkness cycles in an organism's environment. At the cellular level, the circa-24h rhythmicity is generated by a molecular clock based on a transcription-translation feedback network and consists of a cell-autonomous and self-sustained oscillator. In conditions where cells proliferate, the cell division cycle can be also considered as an oscillator. Since both processes run with similar periods in several mammalian cells, it is reasonable to expect that interactions between these two cycles may cause synchronization. Many studies reported evidences of interactions between the circadian and the cell cycles in different organisms. In particular, it appeared that in several systems, specific cell cycle phases occur in distinct temporal windows rather than being randomly distributed in time. These findings led to the concept of circadian gating of the cell cycle, through which the circadian clock can favor or forbid cell cycle transitions at specific circadian phases. However, it was also reported the converse, namely an effect of cell division on the circadian oscillator. Even though interactions between the circadian clock and the cell cycle have been identified in both directions, the dynamical consequences and the directionality of the coupling at the single-cell level were not extensively investigated. In order to better characterize the potential synchronization in mammalian cells, we estimated the mutual interactions between circadian clock and cell cycle in NIH3T3 mouse fibroblasts by the use of time-lapse fluorescent microscopy in combination with statistical analysis and mathematical modeling. NIH3T3 cells, harboring a fluorescent reporter under the control of the circadian RevErb-a gene promoter, were imaged for several days allowing the simultaneous detection of circadian oscillations and time of divisions. The analysis of thousands of circadian cycles in dividing cells indicated that both oscillators are synchronized, with cell divisions occurring about 5 h before the peak of the circadian RevErb-a reporter. We tested several perturbations such as different serum concentrations, different temperatures, treatment with pharmacological compounds and shRNA-mediated knockdown of circadian regulators. Surprisingly, this showed that circadian rhythm and cell cycle remain synchronized over the wide range of conditions probed. Our data showed that this synchronization state reflects an unexpected predominant influence of the cell cycle on the circadian oscillator, and did not support the leading hypothesis about a circadian gating of the cell cycle. The stochastic modeling of two interacting phase oscillators allowed us to identify the parameters of the coupling functions, revealing an acceleration of circadian phase after the division. The work presented in this thesis sheds light on the interaction between two fundamentally recurrent cellular processes in mammalian cells and provides a deeper understanding of the role of the circadian clock in proliferating cells and tissues. These findings might have significant implications for chronobiology and chronotherapeutics.

EPFL2016

Circadian rhythm and cell cycle

Rosamaria Cannavo

EPFL2016