PERIOD DOUBLING SCENARIO EXHIBIT ON ARTIFICIAL NEURAL NETWORK MODEL
Abstract
In this paper we consider a two dimensional nonlinear artificial neural model of memory with as control parameter. Here we investigate the existence of dynamical behaviour of period-doubling route that leads to chaos. We create a suitable C-programming and use Mathematica software to study period doubling route to chaos. The bifurcation points have been calculated numerically and have been observed that the map follows a universal behavior that has been proposed by Feigenbaum. With the help of experimental bifurcation points the accumulation point where chaos starts has been calculated.
Keywords: Periodic points, Bifurcation, Feigenbaum universal Constant,AccumulationPoint
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] Beddington,J.R., Free,C.A., Lawton, J.H., “Dynamic Complexity in Predator-Prey models framed in difference equations”, Nature, 225(1975),58-60.
] Chartier, S., et al. “A nonlinear dynamic artificial neural network model of memory”.New Ideas in Psychology (2007), doi:10.1016/j.newideapsych.2007.07.005
] Dutta,T.K,Bhattacharjee.D, “Bifurcation points, Lyapunov exponent and Fractal dimensions in a two dimensional non linear map”
] Feigenbaum,M.J., “Qualitative Universility for a class of non-linear transformations”,J.Statist.Phys,19:1(1978),25-52.
] Feigenbaum,M.J.,“ Universility Behavior in non-linear systems”,Los Alamos Science,1.(1980),4-27.
] Henon.M, “A two dimensional mapping with a strange attractor”,Commun.Math Phys.50:69-77,1976.
] Hilborn, R.C., “Chaos and Non-linear dynamics”,Oxford Univ.Press.1994.
] Kujnetsov,Y., “Elements of Applied Bifurcation Theory”,Springer(1998).
] May,R.M.,“Simple Mathematical Models With Very Complicated Dynamics”, Nature,Vol.261(1976),459.
] SarmahH.K,Paul. R “Period-doubling route to chaos in a two parameter invertible map with constant jacobian”,IJRRAS3(1), 72-82,April 2010.
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