Jordi Garcia Ojalvo
Edifici GAIA, despatx 1.04
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Research topics & PublicationsStochastic and Nonlinear Dynamics of Biological Systems
Life is inherently dynamical. Furthermore, living systems are usually subject to a substantial
amount of random fluctuations, both of intrinsic and extrinsic origin. Cells, for instance, must
be able to detect and process different kinds of information, either in isolation or as a result
of a collective endeavour. In that context, issues such as
synchronization of dynamical behavior, entrainment to external signals and processing of information
at both single-cell and population levels become relevant (and so far largely unanswered) questions. The figure on
the left shows a colony of Bacillus subtilis cells undergoing sporulation (in white) and competence (in red).
We have found that competence is an inherently dynamical state, triggered stochastically,
that arises as an excitable response to stress. More information
of this particular problem can be found here.
Dynamics and Synchronization in Optical Systems
Optical devices, and particularly lasers, are dynamical systems where nonlinearities
frequently play a relevant role. Additionally, they can usually be described very
precisely, both experimentally (since applied interest has strongly driven the
development of well controlled photonic technologies in the last decades) and
theoretically (with models based on the foundations of quantum optics and
solid-state physics). For those reasons, optical devices are routinely used as
model systems in studies of nonlinear dynamics. Such studies include chaotic and
stochastic dynamics, spatiotemporal dynamics (see below) and synchronization.
The figure on the right shows the encoded, transmitted and decoded signal in
a communication system based on the synchronization of optical spatiotemporal
chaos. More information on this particular application can be found
here.
Stochastic Dynamics and Nonequilibrium Statistical Mechanics
Usually, noise is a disordering agent in dynamical systems. But when
nonequilibrium systems are driven externally by random fluctuations, counterintuitive
phenomena may arise, in the form of noise-induced order. In those cases, an increase in
the amount of noise may lead to a more ordered behavior. Order here
refers to spatial order, and includes stationary spatially homogeneous (but
nontrivial) states (noise-induced phase transitions), stationary heterogenous
structures (noise-sustained patterns), and spatiotemporal states (noise-induced
propagation).
The figure on the left shows an example of noise-induced stripe patterns in the
stochastic Swift-Hohenberg model.
A review of this topic can be found here.
Noise in Excitable Media
Excitable systems are characterized by responding dramatically to small perturbations.
Thus, they are by nature highly susceptible to noise. In the presence of spatial
coupling, they allow the reliable propagation of excitable pulses and structures, such
as wavefronts and spiral waves. Externally applied noise has been
shown to have a relevant influence in this spatiotemporal dynamics, leading for instance
to spiral breakup (related with ventricular
fibrillation), to new mechanisms of coherence resonance, and to excitability in bistable
and even oscillatory media.
The figure on the right shows an example of spiral breakup in a standard FitzHugh-Nagumo
model of excitable media.
A review of this topic can be found here.
Spatiotemporal Dynamics of Lasers
Pattern formation is one of the most striking examples of self-organization in
nature. Many efforts have been devoted in the last decades to understand the
mechanisms and characteristics of pattern-formation processes. Broad-area lasers
provide an excellent framework for these studies, given the controllability
of laser systems (both experimental and theoretical, as explained above).
Phenomena such as modulational instabilities, pattern selection, coupled
pattern formation and localized structures have been studied in this field.
The figure on the left shows the phase profile of a broad-area laser whose
emission occurs in terms of interacting cavity solitons. More information
on this particular phenomenon can be found
here.
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