The Experts below are selected from a list of 102 Experts worldwide ranked by ideXlab platform

E. M. Maslov - One of the best experts on this subject based on the ideXlab platform.

Alessandro Torcini - One of the best experts on this subject based on the ideXlab platform.

  • Stability of splay states in globally coupled rotators.
    Physical Review E, 2009
    Co-Authors: Massimo Calamai, Antonio Politi, Alessandro Torcini
    Abstract:

    The stability of dynamical states characterized by a uniform firing rate (splay states) is analyzed in a network of N globally pulse-coupled rotators (neurons) subject to a generic velocity field. In particular, we analyze short-wavelength modes that were known to be marginally stable in the infinite N limit and show that the corresponding Floquet Exponent scale as 1/N 2 . Moreover, we find that the sign, and thereby the stability, of this spectral component is determined by the sign of the average derivative of the velocity field. For leaky-integrate-and-fire neurons, an analytic expression for the whole spectrum is obtained. In the intermediate case of continuous velocity fields, the Floquet Exponents scale faster than 1/N 2 (namely, as 1/N 4 ) and we even find strictly neutral directions in a wider class than the sinusoidal velocity fields considered by Watanabe and Strogatz [Physica D 74, 197 (1994)].

  • Stability of the splay state in pulse--coupled networks
    arXiv: Disordered Systems and Neural Networks, 2007
    Co-Authors: Rüdiger Zillmer, Antonio Politi, Roberto Livi, Alessandro Torcini
    Abstract:

    The stability of the dynamical states characterized by a uniform firing rate ({\it splay states}) is analyzed in a network of globally coupled leaky integrate-and-fire neurons. This is done by reducing the set of differential equations to a map that is investigated in the limit of large network size. We show that the stability of the splay state depends crucially on the ratio between the pulse--width and the inter-spike interval. More precisely, the spectrum of Floquet Exponents turns out to consist of three components: (i) one that coincides with the predictions of the mean-field analysis [Abbott-van Vreesvijk, 1993]; (ii) a component measuring the instability of "finite-frequency" modes; (iii) a number of "isolated" eigenvalues that are connected to the characteristics of the single pulse and may give rise to strong instabilities (the Floquet Exponent being proportional to the network size). Finally, as a side result, we find that the splay state can be stable even for inhibitory coupling.

  • Stability of the splay state in pulse-coupled networks.
    Physical Review E, 2007
    Co-Authors: Rüdiger Zillmer, Antonio Politi, Roberto Livi, Alessandro Torcini
    Abstract:

    The stability of the dynamical states characterized by a uniform firing rate (splay states) is analyzed in a network of globally coupled leaky integrate-and-fire neurons. This is done by reducing the set of differential equations to a map that is investigated in the limit of large network size. We show that the stability of the splay state depends crucially on the ratio between the pulse width and the interspike interval. More precisely, the spectrum of Floquet Exponents turns out to consist of three components: (i) one that coincides with the predictions of the mean-field analysis [Abbott and van Vreesvijk, Phys. Rev. E 48, 1483 (1993)], (ii) a component measuring the instability of ``finite-frequency'' modes, (iii) a number of ``isolated'' eigenvalues that are connected to the characteristics of the single pulse and may give rise to strong instabilities (the Floquet Exponent being proportional to the network size). Finally, as a side result, we find that the splay state can be stable even for inhibitory coupling.

Frank Ellinger - One of the best experts on this subject based on the ideXlab platform.

  • A Feedback Spin-Valve Memristive System
    IEEE Transactions on Circuits and Systems I: Regular Papers, 2012
    Co-Authors: Torsten Schmidt, Udo Jorges, Frank Ellinger
    Abstract:

    We propose theoretically a generalized memristive system based on controlled spin polarizations in giant magnetoresistive material using a feedback loop with classical Hall Effect. The dynamics can exhibit a memristive pinched hysteretic loop while it possesses a self-crossing knot not located at the origin. Additionally, a single-looped orbit can also be observed in the system. We provide a sufficient condition for the stability based on an estimation of the Floquet Exponent. The analysis shows that the non-origin-crossing dynamics is generally permitted in a class of passive memory systems that are not subject to Ohm's Law. We further develope the prevailing homogeneous definition to a broadened concept of generalized heterogeneous memristive systems, permitting the self-crossing knot not located at the origin, and ultimately to the concept of compound memory electronic systems.

V. A. Koutvitsky - One of the best experts on this subject based on the ideXlab platform.

K Pyragas - One of the best experts on this subject based on the ideXlab platform.

  • Analytical properties and optimization of time-delayed feedback control.
    Physical review. E Statistical nonlinear and soft matter physics, 2002
    Co-Authors: K Pyragas
    Abstract:

    Time-delayed feedback control is an efficient method for stabilizing unstable periodic orbits of chaotic systems. If the equations governing the system dynamics are known, the success of the method can be predicted by a linear stability analysis of the desired orbit. Unfortunately, the usual procedures for evaluating the Floquet Exponents of such systems are rather intricate. We show that the main stability properties of the system controlled by time-delayed feedback can be simply derived from a leading Floquet Exponent defining the system behavior under proportional feedback control. Optimal parameters of the delayed feedback controller can be evaluated without an explicit integration of delay-differential equations. The method is valid for low-dimensional systems whose unstable periodic orbits are originated from a period doubling bifurcation and is demonstrated for the Rössler system and the Duffing oscillator.

  • Analytical properties and optimization of time-delayed feedback control.
    Physical Review E, 2002
    Co-Authors: K Pyragas
    Abstract:

    Semiconductor Physics Institute, LT-2600 Vilnius, Lithuania~Received 11 April 2002; published 19 August 2002!Time-delayed feedback control is an efficient method for stabilizing unstable periodic orbits of chaoticsystems. If the equations governing the system dynamics are known, the success of the method can bepredicted by a linear stability analysis of the desired orbit. Unfortunately, the usual procedures for evaluatingthe Floquet Exponents of such systems are rather intricate. We show that the main stability properties of thesystem controlled by time-delayed feedback can be simply derived from a leading Floquet Exponent definingthe system behavior under proportional feedback control. Optimal parameters of the delayed feedback control-ler can be evaluated without an explicit integration of delay-differential equations. The method is valid forlow-dimensional systems whose unstable periodic orbits are originated from a period doubling bifurcation andis demonstrated for the Ro¨ssler system and the Duffing oscillator.DOI: 10.1103/PhysRevE.66.026207 PACS number~s!: 05.45.Gg, 02.30.Yy, 02.30.KsI. INTRODUCTION