Loading presentation...

Present Remotely

Send the link below via email or IM

Copy

Present to your audience

Start remote presentation

  • Invited audience members will follow you as you navigate and present
  • People invited to a presentation do not need a Prezi account
  • This link expires 10 minutes after you close the presentation
  • A maximum of 30 users can follow your presentation
  • Learn more about this feature in our knowledge base article

Do you really want to delete this prezi?

Neither you, nor the coeditors you shared it with will be able to recover it again.

DeleteCancel

Make your likes visible on Facebook?

Connect your Facebook account to Prezi and let your likes appear on your timeline.
You can change this under Settings & Account at any time.

No, thanks

Chaos theory and Artificial Neural Network

No description
by

Amin Hosseiny Marani

on 29 September 2012

Comments (0)

Please log in to add your comment.

Report abuse

Transcript of Chaos theory and Artificial Neural Network

y = -b1*x+c1 y = b2*x+c2 y = b3*x + c3 - 0 + (1) (2) (3) (4) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29) L. A. Aguirre and C. Letellier, “Modeling Nonlinear Dynamics and Chaos : A Review,” Mathematical Problems in Engineering, vol. 2009, 2009.
Auslander, J., Bhatia, N.P., Seibert, P. [1964]: Attractors in dynamical systems, Bol. Soc. Mat. Mex. 9, 55-66.
Grebogi, Ott, Pelikan, Yorke (1984). "Strange attractors that are not chaotic". Physica D 13: 261–268. doi:10.1016/0167-2789(84)90282-3.
Conley, C. [1978]: "Isolated Invariant Sets and the Morse Index," C.B.M.S. Regional Lect. 38, A.M.S.
www.wikipedia.org
www.scholarpedia.com
J.E. Flaherty, F.C. Hoppensteadt, Frequency entrainment of a forced van der Pol oscillator, Studies in Appl. Math., 58, 5-15, 1978.
P. C. R. Ã, ―Chaos and hyper chaos in a Hopfield neural network,‖ Neurocomputing, vol.
. 4, no. 1., pp. 3361-3364, 2011.
 
Ruelle, David (August 2006). "What is...a Strange Attractor?" (PDF). Notices of the American Mathematical Society 53 (7): 764–765. Retrieved 2008-01-16.
Woolley, J. W., Agarwal, P. K., & Baker, J. (2010). Modeling and prediction of chaotic systems with artificial neural networks, (July 2009), 989-1004.
Krishnaiah, J., Kumar, C. S., & Faruqi, M. a. (2006). Modelling and control of chaotic processes through their Bifurcation Diagrams generated with the help of Recurrent Neural Network models: Part 1—simulation studies. Journal of Process Control, 16(1), 53-66. 2005.04.002
Dudul, S. V. (2005). Prediction of a Lorenz chaotic attractor using two-layer perceptron neural network. Applied Soft Computing, 5(4), 333-355. 2004.07.005.
Kaslik, E., & Balint, S. (2009). Complex and chaotic dynamics in a discrete-time-delayed Hopfield neural network with ring architecture. Neural Networks, 22(10), 1411-1418. Elsevier Ltd.2009.03.009
Han, M., & Wang, Y. (2009). Analysis and modeling of multivariate chaotic time series based on neural network. Expert Systems With Applications, 36(2), 1280-1290. Elsevier Ltd. 2007.11.057
W.-zhi Huang, “CHAOS , BIFURCATION AND ROBUSTNESS OF A CLASS OF HOPFIELD NEURAL NETWORKS,” IJBC, vol. 21, no. 3, pp. 885-895, 2011.
Zheng, P., Ã, W. T., & Zhang, J. (2010). Some novel double-scroll chaotic attractors in Hopfield networks. Neurocomputing, 73(10-12), 2280-2285. Elsevier. 2010.02.015
Torres, J., & Cort, M. (2007). Chaotic hopping between attractors in neural networks. Neural Networks, 20, 230-235. 2006.11.005.
Min, X., Jian’an, F., Yang, T., & Zhijie, W. (2010). Dynamic depression control of chaotic neural networks for associative memory. Neurocomputing, 73(4-6), 776-783.
L. Shen and M. Wang, “Adaptive control of chaotic systems based on a single layer neural network,” Physics Letters A, vol. 368, no. 5, pp. 379-382, Aug. 2007.
G. He, L. Chen, and K. Aihara, “Associative memory with a controlled chaotic neural network,” Neurocomputing, vol. 71, no. 13–15, pp. 2794-2805, Aug. 2008.
Huang, Z., Mohamod, S., & Bin, H. (2010). Multiperiodicity analysis and numerical simulation of discrete-time transiently chaotic non-autonomous neural networks with time- varying delays. Communications in Nonlinear Science and Numerical Simulation, 15(5), 1348-1357. Elsevier B.V. 2009.05.060.
Sussillo, D., & Abbott, L. F. (2009). Generating Coherent Patterns of Activity from Chaotic Neural Networks. Neuron, 63(4), 544-557. Elsevier Ltd. 2009.07.018
J. M. Bahi, J. Couchot, C. Guyeux, and M. Salomon, “Neural networks and chaos : Construction , evaluation of chaotic networks , and prediction of chaos with multilayer feedforward networks Neural networks and chaos : Construction , evaluation of chaotic networks , and prediction of chaos with multilayer fe,” vol. 013122, no. May, 2012.
Jaeger, H., and Haas, H. (2004). Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication. Science 304, 78–80.
Jaeger, H., and Haas, H. (2004). Harnessing nonlinearity: predicting chaotic
Full transcript