AUGIER , Nicolas

In this paper, we consider a system driven by a controlled Schrödinger equation with two external control inputs. Motivated by applications to the control of quantum systems having conical or semi-conical eigenvalue intersections, we propose to study the singularities and the parametric bifurcations of the associated non-mixing field, along...

We study the minimal-time problem for a piecewise affine bistable switch. Motivated by applications in synthetic biology and biotechnology, the aim is to minimize the time needed for this system to achieve transitions between its two stable steady states. The latter represents the two possible states of a genetic toggle switch, a synthetic...

In this preliminary work we give a geometric characterization of the time-optimal trajectories for a piecewise affine bistable switch. Such hybrid models play a major role in systems biology, as they can expressively account for the behaviors of simple gene-regulatory networks. A key example of these biological circuits is the genetic toggle...

We study the minimal-time problem for a piecewise affine bistable switch. Motivated by applications in synthetic biology and biotechnology, the aim is to minimize the time needed for this system to achieve transitions between its two stable steady states. The latter represents the two possible states of a genetic toggle switch, a synthetic...

In this paper, we study the diffusive coupling of a network of identical bistable switch piecewise-affine systems. We propose a control strategy which synchronizes every bistable switch subsystem of the network towards the same steady state.

In this paper we investigate the emergent dynamics in a network of N coupled cells, each expressing a similar genetic bistable switch. The bistable switch is modeled as a piecewise affine system and the cells are diffusively coupled. We show that both the coupling topology and the strength of the diffusion parameter may introduce new steady...

The study of synchronization in coupled genetic networks is a very challenging topic that is usually analyzed on a case-by-case basis. Here we consider a general model of genetic networks and examine two forms of interconnection, either homogeneous or heterogeneous coupling, corresponding to coupling functions that are either equal or different...

In this paper we study up to which extent we can apply adiabatic control strategies to a quantum control model obtained by rotating wave approximation. In particular, we show that, under suitable assumptions on the asymptotic regime between the parameters characterizing the rotating wave and the adiabatic approximations, the induced flow...

In the physics literature it is common to see the rotating wave approximation and the adiabatic approximation used "in cascade" to justify the use of chirped pulses for two-level quantum systems driven by one external field, in particular when the resonance frequency of the system is not known precisely.Both approximations need relatively long...