We study the stochastic properties of gene regulation taking into account the non-Markovian character of gene transcription and translation. We show that time delay in protein production or degradation may change the behavior of the system from stationary to oscillatory even when a deterministic counterpart of the stochastic system exhibits no oscillations. Assuming significant decorrelation on the time scale of gene transcription, we deduce a truncated master equation of the reactive system and derive an analytical expression for the autocorrelation function of the protein concentration. For weak feedback the theory agrees well with with numerical simulations based on the modified direct Gillespie method.
We describe a concept in which an array of coupled nonlinear
oscillators is used for beamforming in phased array receivers. The
signal that each sensing element receives, beam steered by time
delays, is input to a nonlinear oscillator. The nonlinear
oscillators for each element are in turn coupled to each other.
For incident signals sufficiently close to the steering angle, the
oscillator array will synchronize to the forcing signal whereas
more obliquely incident signals will not induce synchronization.
The beam pattern that results can show a narrower mainlobe and
lower sidelobes than the equivalent conventional linear
beamformer. We present a theoretical analysis to explain the beam
pattern of the nonlinear oscillator array.
The chaotic spike train of a homoclinic dynamical system is self-synchronized by applying a time delayed correction proportional to the laser output intensity. Due to the sensitive nature of the homoclinic chaos to external perturbations, stabilization of very long periodic orbits is possible. On these orbits, the dynamics appears chaotic over a finite time, but then it repeats with a recurrence time that is slightly longer than the delay time. The effect, called delayed self-synchronization (DSS), displays analogies with neurodynamic events which occur in the build-up of long term memories.
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