26 research outputs found
The effects of delay on the HKB model of human motor coordination
Understanding human motor coordination holds the promise of developing
diagnostic methods for mental illnesses such as schizophrenia. In this paper,
we analyse the celebrated Haken-Kelso-Bunz (HKB) model, describing the dynamics
of bimanual coordination, in the presence of delay. We study the linear
dynamics, stability, nonlinear behaviour and bifurcations of this model by both
theoretical and numerical analysis. We calculate in-phase and anti-phase limit
cycles as well as quasi-periodic solutions via double Hopf bifurcation analysis
and centre manifold reduction. Moreover, we uncover further details on the
global dynamic behaviour by numerical continuation, including the occurrence of
limit cycles in phase quadrature and 1-1 locking of quasi-periodic solutions.Comment: Submitted to the SIAM Journal on Applied Dynamical Systems. 27 pages,
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Parametric resonance in the Rayleigh-Duffing oscillator with time-delayed feedback
We investigate the principal parametric resonance of a Rayleigh–Duffing oscillator with
time-delayed feedback position and linear velocity terms. Using the asymptotic perturbation
method, we obtain two slow flow equations on the amplitude and phase of the oscillator.
We study the effects of the frequency detuning, the deterministic amplitude, and the
time-delay on the dynamical behaviors, such as stability and bifurcation associated with
the principal parametric resonance. Moreover, the appropriate choice of the feedback gain
and the time-delay is discussed from the viewpoint of vibration control. It is found that the
appropriate choice of the time-delay can broaden the stable region of the non-trivial
steady-state solutions and enhance the control performance. Theoretical stability analysis
is verified through a numerical simulation.The University of Pretoriahttp://www.elsevier.com/locate/cnsnsai201
Parameters Identification and Synchronization of Chaotic Delayed Systems Containing Uncertainties and Time-Varying Delay
Time delays are ubiquitous in real world and are often sources of complex behaviors of dynamical systems. This paper addresses the problem of parameters identification and synchronization of uncertain chaotic delayed systems subject to time-varying delay. Firstly, a novel and systematic adaptive scheme of synchronization is proposed for delayed dynamical systems containing uncertainties based on Razumikhin condition and extended invariance principle for functional differential equations. Then, the proposed adaptive scheme is used to estimate the unknown parameters of nonlinear delayed systems from time series, and a sufficient condition is given by virtue of this scheme. The delayed system under consideration is a very generic one that includes almost all well-known delayed systems (neural network, complex networks, etc.). Two classical examples are used to demonstrate the effectiveness of the proposed adaptive scheme