ELFT HÍRADÓ

[StatFizSzeminar <statfiz AT glu.elte.hu>]

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           ELTE TTK Fizikai Intézet
       STATISZTIKUS FIZIKAI SZEMINÁRIUM


             2019. szeptember 25.

                   szerda 

                   11.00

                Ulrike Feudel

        Carl von Ossietzky University



"Transient chaos in networked systems: 
Desynchronization and state-dependent 
            vulnerability"

We analyze the final state sensitivity of
nonlocal networks of Duffing oscillators 
with respect to the initial conditions of 
their units. By changing the initial 
conditions of a single network unit, we 
perturb an initially synchronized state, 
which is the only attractor for a single 
unit. Depending on the perturbation strength,
we observe the existence of two possible 
network long-term states: (i) The network 
neutralizes the perturbation effects and 
returns to its synchronized configuration. 
(ii) The perturbation leads the network to
an alternative desynchronized state. By 
computing uncertainty exponents of a two-
dimensional cross section of the state space,
we find the existence of a fractal set of 
initial conditions converging to this d
esynchronized solution, which appears to be 
either a new attractor or a chaotic saddle, 
i.e. an unstable chaotic set on which 
trajectories persist for extremely long times.
Furthermore, we report the existence of an 
intricate time dependence of the vulnerability
of the synchronized states in a network composed
of identical electronic circuits. By perturbing
the synchronized dynamics in consecutive 
instants of time, we find that synchronization
breaks down for some time instants while it 
persists for others. The mechanism behind this
intriguing phenomenon is again the existence 
of an unstable chaotic set close to the s
ynchronized trajectory. Both phenomena 
highlight the crucial role played by unstable
chaotic set leading to transient chaotic 
dynamics in networked systems. We discuss 
that these phenomena are generic for large 
classes of nonlinear dynamical systems.



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