Abstract
The simplest example of a dynamical system which organizes itself through cooperation and competition has been given in this conference C8]; I shall formalize it as follows: let A be a linear operator in the plane R 2,and consider the ordinary diferential system
where x is constrained to remain in the unit square
Keywords
- Nonlinear Evolution Equation
- Random Wave
- Liapunov Function
- Secondary Bifurcation
- NeurophysioLogiCaL modeLs
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References
E. Bienenstock, Cooperation and competition in the central system development: a unifying approach, (1984) in Synergetics, Springer.
E.Bienenstock, this volume.
E.Bienenstock, M.Schatzman, B.Moore, Nonlinear systems with a spatial convolution term in a model of development of neuronal selectivity, to appear.
F.Comets, T.Eisele, M.Schatzman, On secondary bifurcations for some nonlinear convolution equations, to appear, Trans. A.M.S. Soc.
T.Eisele, R.Ellis, Symmetry breaking and random waves for magnetic systems on a circle, Z. Wahrsch. Verw- Gebiete,63(1983)297–348.
M.Schatzman, E.Bienenstock, Neurophysiological models, Spin models, and pattern formation, preprint, 1984.
N.V.Swindale, A model for the formation of ocular dominance stripes, Proc. R. Soc. Lond. B, 208(1980)243–264.
Anderson, this volume
C. von der Malsburg, this volume.
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Schatzman, M. (1986). Self Organizing Mathematical Models: Nonlinear Evolution Equations with a Convolution term. In: Bienenstock, E., Soulié, F.F., Weisbuch, G. (eds) Disordered Systems and Biological Organization. NATO ASI Series, vol 20. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82657-3_38
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DOI: https://doi.org/10.1007/978-3-642-82657-3_38
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