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  • American Institute of Physics (AIP)  (3)
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  • 1
    Electronic Resource
    Electronic Resource
    Homoclinic bifurcation in a Hodgkin–Huxley model of thermally sensitive neurons (2000)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 10 (2000), S. 231-239 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We study global bifurcations of the chaotic attractor in a modified Hodgkin–Huxley model of thermally sensitive neurons. The control parameter for this model is the temperature. The chaotic behavior is realized over a wide range of temperatures and is visualized using interspike intervals. We observe an abrupt increase of the interspike intervals in a certain temperature region. We identify this as a homoclinic bifurcation of a saddle-focus fixed point which is embedded in the chaotic attractors. The transition is accompanied by intermittency, which obeys a universal scaling law for the average length of trajectory segments exhibiting only short interspike intervals with the distance from the onset of intermittency. We also present experimental results of interspike interval measurements taken from the crayfish caudal photoreceptor, which qualitatively demonstrate the same bifurcation structure. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.166488
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  • 2
    Electronic Resource
    Electronic Resource
    Characterizing strange nonchaotic attractors (1995)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 5 (1995), S. 253-260 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Strange nonchaotic attractors typically appear in quasiperiodically driven nonlinear systems. Two methods of their characterization are proposed. The first one is based on the bifurcation analysis of the systems, resulting from periodic approximations of the quasiperiodic forcing. Second, we propose to characterize their strangeness by calculating a phase sensitivity exponent, that measures the sensitivity with respect to changes of the phase of the external force. It is shown that phase sensitivity appears if there is a nonzero probability for positive local Lyapunov exponents to occur. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.166074
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  • 3
    Electronic Resource
    Electronic Resource
    Multistability and the control of complexity (1997)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 7 (1997), S. 597-604 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We show how multistability arises in nonlinear dynamics and discuss the properties of such a behavior. In particular, we show that most attractors are periodic in multistable systems, meaning that chaotic attractors are rare in such systems. After arguing that multistable systems have the general traits expected from a complex system, we pass to control them. Our controlling complexity ideas allow for both the stabilization and destabilization of any one of the coexisting states. The control of complexity differs from the standard control of chaos approach, an approach that makes use of the unstable periodic orbits embedded in an extended chaotic attractor. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.166259
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