[PPT] - Controlled Synchronisation of Dynamical Systems Antonio Loria, Elena PowerPoint Presentation

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Controlled Synchronisation

f Dynamical Systems

European Embedded Control Institute Graduate School –8th ed. Antonio Loria, Elena Panteley

C.N.R.S., France loria@lss.supelec.fr panteley@lss.supelec.fr

Gif, Jan. 24-29 2011

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SYNCHRONISATION ?

Etymology: σ´ υν –same; χρ´

νoς –time

sharing the same time; occurring at the same time what occurs at the same time ? two processes; two phenomena; two events; two only? instantaneous events, phenomena, processes? REPETITIVE i.e. periodic? . . . RYTHM

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RYTHM. . . Are the rythms and the events independent of each other or

are they somehow connected ?

Synchronisation is

the adjustment of rythms of repetitive events (phenomena, processes) through weak interaction; the mutual time-conformity of two or more processes (events, phenomena) INTERACTION REPETITIVENESS RYTHM

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Interaction, Repetitiveness, Rythm

Repetition of a motion pattern; passes through a “point” (or infinitessimaly close to it) infinitely many times; depends only on its own parameters and dynamics (no external stimuli); does not depend on the initial conditions . . .

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Interaction, Repetitiveness, Rythm

Repetition of a motion pattern; passes through a “point” (or infinitessimaly close to it) infinitely many times; depends only on its own parameters and dynamics (no external stimuli); does not depend on the initial conditions . . .

OSCILLATION

COUPLING clocks . . .

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Synchronization is . . .

The interaction of rythms of oscillating objects due to their weak interaction interaction must occur through a weak coupling; two synchronized oscillators must be separable into two self-sustained processes; adjustment is entailed and sustained through interaction; a small mismatch in the systems’ motions entails small variations in the synchronisation (stability) How does interaction takes place? What are the forms of coupling? can it be modified?

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Examples of synchrony:

neuron firing; flocks of migrating birds; banks of fish; fireflies; biological clocks; menstruation cycles; heart beating; an orchestra . . .

Coupling:

cicardian rythm is connected with day/night and seasonal luminance variations; fireflies’ lightening is influenced by those of their neighbours; violonists hear the sound of their own violins and of others’

Keywords

Clock, Oscillator, Interaction, Cycle, Repetitiveness, Periodicity, Rythm, Simultaneity, Stability, Motion, Trajectory

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SLIDE 8

Research aereas

Biology

enthomology, molecular biology, clocks, zoology, medicine

Physics

Nonlinear phenomena,

scillations, chaos

Circuit theory

van der Pol, Duffing, L¨ u, Chen, Colpitts . . .

Engineering

Cooperative systems, teleoperation, robotics formation control,

UAVs, (sub)marine,
platooning,

Computer Science

Networks band allocation, clocks, . . .

Communications

SYNC

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SLIDE 9