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Biomedical subjects

M Tlidi

Publications and source records attributed to M Tlidi.

8 recordsLinked to original sources
PubMed2004

Bistability between different localized structures in nonlinear optics.

We report the observation of different localized structures coexisting for the same parameter values in an extended system. The experimental findings are carried out in a nonlinear optical interferometer and are fully confirmed by numerical simulations. The existence of each kind of localized structure is put in relation to a corresponding delocalized pattern observed. A quantitative evaluation of the range of pump parameter allowing bistability between localized structures is given. The phenomenon reported results to be robust in parameter space.

Journal Article↗
PubMed2004

Optical patterns with different wavelengths.

The semiconductor resonator is an example of an optical system where two modulational instabilities with different wave numbers coexist. In the limit of nascent bistability, the dynamics is generically described by a nonvariational real order parameter equation, of which we give a detailed derivation. This considerably simplifies the linear and weakly nonlinear stability analyses. When the two instabilities are close together, we derive normal form equations and put special emphasis on "envelope" branches of solutions. These particular solutions may connect the two instability points or form an isola. On the basis of these rigorous results, we finally discuss the case of distant modulational instabilities, in both one and two transverse dimensions.

Journal Article↗
PubMed2003

Interaction of two modulational instabilities in a semiconductor resonator.

The interaction of two neighboring modulational instabilities in a coherently driven semiconductor cavity is investigated. First, an asymptotic reduction of the general equations is performed in the limit of a nearly vertical input-output characteristic. Next, a normal form is derived in the limit where the two instabilities are close to one other. An infinity of branches of periodic solutions are found to emerge from the unstable portion of the homogeneous branch. These branches have a nontrivial envelope in the bifurcation diagram that can either smoothly join the two instability points or form an isolated branch of solutions.

Journal Article↗
PubMed2002

Curvature instability in passive diffractive resonators.

We study the stability of localized structures in a passive optical bistable system. We show that there is a critical value of the input field intensity above which localized structures are unstable with respect to a curvature instability. Beyond this instability boundary, a transition from the localized branch of solutions to stable hexagons is found.

Journal Article↗
PubMed2002

Localized vegetation patches: a self-organized response to resource scarcity.

We show that spatial self-organization allows vegetation to survive greater resource limitation. Isolated vegetation patches observed in nutrient-poor territories of South America and West Africa are interpreted as localized structures arising from the bistability between the bare state and the patchy vegetation state.

Africa, Western↗