A chaotic system with available prior knowledge is identified with both the sequential hybrid neural network and the standard Artificial Neural Network (ANN). The identified models are validated with phase portrait, return map, the largest Lyapunov exponent and correlation dimension instead of using Sum of Square Errors (SSE). Interpolation and Extrapolation capability of the models ate compared. This is demonstrated for nonisothermal, irreversible, first-order, series reaction A-->B-->C in a CSTR.

Chaos Hybrid Neural Network Modified Error Back Propagation System Identification Validation

Abarbanel HDI, Brown R, Sidorowich JJ, Tsimring LS, Rev. Mod. Phys., 65(4), 1331 (1993) 
Adomaitis RA, Farber RM, Hudson JL, Kevrekidis IG, Kube M, Lapedes AS, "Application of Neural Nets to System Identification and Bifurcation Analysis of Real World Experimental Data," In: Neural Networks: Biological Computers of Electronic Brains, Springer Verlag, Paris, 87 (1990)
Aguirre LA, Billings SA, Int. J. Bifurcation Chaos, 4(1), 109 (1994) 
Casdagli M, Physica D, 35, 335 (1989) 
Doedel EJ, "AUTO: Software for Continuation and Bifurcation Problems in Ordinary Differential Equations," AUTO 86 User Manual, CALTECH (1986)
Farmer JD, Ott E, Yorke JA, "The Dimensions of Chaotic Attractors," Physica 7D, 153 (1983)
Giona M, Lentini F, Cimagalli V, Phys. Rev., A, 44, 3496 (1991) 
Grassberger P, Procaccia I, Physica D, 9, 189 (1983) 
Grassberger P, Schreiber T, Schaffrath C, Int. J. Bifurcation Chaos, 1(3), 521 (1991) 
Jordan MI, Rumelhart DE, Cognitive Sci., 16, 307 (1992) 
Kahlert C, Rossler OE, Varma A, Springer Ser. Chem. Phys., 18, 355 (1981)
Kim HJ, "Identification and Validation of Neural Network Models for Chaotic Chemical Reaction Systems," M.S. Thesis, Pohang University of Science and Technology, Korea (1998)
Kim HJ, Chang KS, Comput. Chem. Eng., submitted (1998)
Kim HJ, Lee JS, Han C, Chang KS, "Chaos and Fractals in Process Systems Engineering," Proceedings of the Forty-first Annual Meeting of the ISSS, Seoul (1997)
Packard NH, Crutchfield JP, Farmer JD, Shaw RS, Phys. Rev. Lett., 45(9), 712 (1980) 
Parker TS, Chua LO, "Practical Numerical Algorithms for Chaotic Systems," Springer-Verlag (1989)
Principe JC, Rathie A, Kuo JM, Int. J. Bifurcation Chaos, 2(4), 989 (1992) 
Psaltis D, Sideris A, Yamamura AA, IEEE Cont. Syst. Mag., 4(17) (1988)
Psichogios DC, Ungar LH, AIChE J., 38(10), 1499 (1992) 
Rand DA, Young LS, "Dynamical Systems and Turbulence," Springer Verlag (Berlin), 366 (1981)
Roux JC, Simoyi RH, Swinney HL, "Observation of a Strange Attractor," Physica 8D, 257 (1983)
Rumelhart D, Hinton G, Williams R, "Learning Internal Representations by Error Propagation," Parallel Distributed Processing: Explorations in the Microstructures of Cognition: 1. Foundation, MIT Press (1986)
Sauer T, Yorke JA, Casdagli M, J. Stat. Phys., 65(3-4), 579 (1991) 
Seydel R, "From Equilibrium to Chaos: Practical Bifurcation and Stability Analysis," Elsevier, New York (1988)
Takens F, "Detecting Strange Attractors in Turbulence," in Lecture Notes in Mathematics, vol. 898 eds
Thompson ML, Kramer MA, AIChE J., 40(8), 1328 (1994) 
Wolf A, Swift JB, Swinney HL, Vastano JA, "Determining Lyapunov Exponents from a Time Series," Physica 16D, 285 (1985)