4,877 research outputs found
A new method for the determination of the locking range of oscillators
A time-domain method for the determination of the injection-locking range of oscillators is presented. The method involves three time dimensions: the first and the second are warped time scales used for the free-running frequency and the external excitation, respectively and the third is to account for slow transients to reach a steady-state regime. The locking range is determined by tuning the frequency of the external excitation until the oscillator locks. The locking condition is determined by analyzing the Jacobian matrix of the system. The method is advantageous in that the computational effort is independent of the presence of widely separated time constants in the oscillator. Numerical results for a Van Der Pol oscillator are presented
Application of the method of multiple scales to unravel energy exchange in nonlinear locally resonant metamaterials
In this paper, the effect of weak nonlinearities in 1D locally resonant
metamaterials is investigated via the method of multiple scales. Commonly
employed to the investigate the effect of weakly nonlinear interactions on the
free wave propagation through a phononic structure or on the dynamic response
of a Duffing oscillator, the method of multiple scales is here used to
investigate the forced wave propagation through locally resonant metamaterials.
The perturbation approach reveals that energy exchange may occur between
propagative and evanescent waves induced by quadratic nonlinear local
interaction
Optimal Subharmonic Entrainment
For many natural and engineered systems, a central function or design goal is
the synchronization of one or more rhythmic or oscillating processes to an
external forcing signal, which may be periodic on a different time-scale from
the actuated process. Such subharmonic synchrony, which is dynamically
established when N control cycles occur for every M cycles of a forced
oscillator, is referred to as N:M entrainment. In many applications,
entrainment must be established in an optimal manner, for example by minimizing
control energy or the transient time to phase locking. We present a theory for
deriving inputs that establish subharmonic N:M entrainment of general nonlinear
oscillators, or of collections of rhythmic dynamical units, while optimizing
such objectives. Ordinary differential equation models of oscillating systems
are reduced to phase variable representations, each of which consists of a
natural frequency and phase response curve. Formal averaging and the calculus
of variations are then applied to such reduced models in order to derive
optimal subharmonic entrainment waveforms. The optimal entrainment of a
canonical model for a spiking neuron is used to illustrate this approach, which
is readily extended to arbitrary oscillating systems
Sensitive Dependence on Parameters of Continuous-time Nonlinear Dynamical Systems
We would like to thank the partial support of this work by the Brazilian agencies FAPESP (processes: 2011/19296-1 and 2013/26598-0, CNPq and CAPES. MSB acknowledges EPSRC Ref. EP/I032606/1.Peer reviewedPostprin
Characteristics of in-out intermittency in delay-coupled FitzHugh-Nagumo oscillators
We analyze a pair of delay-coupled FitzHugh-Nagumo oscillators exhibiting
in-out intermittency as a part of the generating mechanism of extreme events.
We study in detail the characteristics of in-out intermittency and identify the
invariant subsets involved --- a saddle fixed point and a saddle periodic orbit
--- neither of which are chaotic as in the previously reported cases of in-out
intermittency. Based on the analysis of a periodic attractor possessing in-out
dynamics, we can characterize the approach to the invariant synchronization
manifold and the spiralling out to the saddle periodic orbit with subsequent
ejection from the manifold. Due to the striking similarities, this analysis of
in-out dynamics explains also in-out intermittency.Comment: 15 pages, 6 figure
Delayed Dynamical Systems: Networks, Chimeras and Reservoir Computing
We present a systematic approach to reveal the correspondence between time
delay dynamics and networks of coupled oscillators. After early demonstrations
of the usefulness of spatio-temporal representations of time-delay system
dynamics, extensive research on optoelectronic feedback loops has revealed
their immense potential for realizing complex system dynamics such as chimeras
in rings of coupled oscillators and applications to reservoir computing.
Delayed dynamical systems have been enriched in recent years through the
application of digital signal processing techniques. Very recently, we have
showed that one can significantly extend the capabilities and implement
networks with arbitrary topologies through the use of field programmable gate
arrays (FPGAs). This architecture allows the design of appropriate filters and
multiple time delays which greatly extend the possibilities for exploring
synchronization patterns in arbitrary topological networks. This has enabled us
to explore complex dynamics on networks with nodes that can be perfectly
identical, introduce parameter heterogeneities and multiple time delays, as
well as change network topologies to control the formation and evolution of
patterns of synchrony
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