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  • Diffusive Lotka-Volterra system  (1)
  • Perron-Frobenius theorem  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Existence and stability of local excitations in homogeneous neural fields (1979)
    Springer
    Journal of mathematical biology 7 (1979), S. 303-318 
    Details
    ISSN: 1432-1416
    Keywords: Neural field ; Waveform stability ; Lateral inhibition ; Dynamics of pattern formation ; Perron-Frobenius theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Summary Dynamics of excitation patterns is studied in one-dimensional homogeneous lateral-inhibition type neural fields. The existence of a local excitation pattern solution as well as its waveform stability is proved by the use of the Schauder fixed-point theorem and a generalized version of the Perron-Frobenius theorem of positive matrices to the function space. The dynamics of the field is in general multi-stable so that the field can keep short-term memory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00275151
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Stable spatio-temporal oscillations of diffusive Lotka-Volterra system with three or more species (1983)
    Springer
    Journal of mathematical biology 18 (1983), S. 213-221 
    Details
    ISSN: 1432-1416
    Keywords: Diffusive Lotka-Volterra system ; Hopf-bifurcation ; Spatiotemporal oscillation ; Stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A stability condition for Hopf-bifurcating solutions from the uniform equilibrium of clasical Lotka-Volterra interaction-diffusion equations is presented. Using this condition, it is shown that stable spatio-temporal oscillations exist in the framework of such equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276088
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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