By Elie Bienenstock (auth.), Prof. Dr. Jean-Pierre Aubin, Prof. Dr. Donald Saari, Prof. Dr. Karl Sigmund (eds.)
Read Online or Download Dynamics of Macrosystems: Proceedings of a Workshop on the Dynamics of Macrosystems Held at the International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria, September 3–7, 1984 PDF
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Additional resources for Dynamics of Macrosystems: Proceedings of a Workshop on the Dynamics of Macrosystems Held at the International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria, September 3–7, 1984
Sample text
N (for columns) . Simulation experiments can be carried out with both deterministic and stochastic "learning rules". In the latter case superimposed noise is also taken into consideration : I S . : = max (0 , S. J ~ • k6) ; i=l, ... ,k; j=l, ... ,l (Note, however, that even in the case where k6 = 0 the model is not completely deterministic since this presynaptic activity is inherently random in character. ) Both normal development and plastic rearrangement of the projections have been simulated by iterating the modification loop.
In this case no equilibrIUm e'dsts: Hand U have destroyed each other. ,;::x,O), u = (-J-A,O) if A < A ~ and A· = O. ;ponds to the 33 "vertical" trajectories converging to U in Figure 3). An example of this in two dimensions is given below (using complex number notation) : z = pei " i =z{f(p) +ig(,,» where the given functions f and 9 have the shape s illustrate d in Figure 4. f1 o Figure 4. The shapes of the functions " f and g. The resulting dynamics in th e phase plane R2 '::: «: are shown in Figure 5.
9. L. Hodgkin and AF. Huxley. A quantitative description of membrane current and its application to conduction and excitation in nerve membranes. J Physial. 117 {1952} 500-544. 10. R. Fitzhugh. Impulses and physiological states in theoretical models of nerve membrane. Biophys. J 1 {1961} 445-466. 11. M. Bramson. Convergence of solutions of the Kolmogorov equation to travelling waves. Memoirs AMS2B5{44} 19B3. II. ECOLOGICAL MODELS PERSISTENCE IN SYSTEMS WITH DIFFUSION V. Hutson! and W. Moran 2 !
