REFERENCES
[1] P. Adams, Hebb and Darwin, Journal of Theor. Biology, 195 (1998), 419-438.
[2] S. Adler, Quaternionic Quantum Mechanics and Quantum Fields, Oxford Univ. Press, New York, 1995.
[3] L. Auslander and R. MacKenzie, Introduction to Differentiable Manifolds, Dover Publications, Inc., 1963.
[4] P. Baldi and K. Hornik, Neural networks and principal component analysis: learning from
examples without local minima, Neural Networks, 2 (1989), 53-58.
[5] T. Blyth and E. Robertson, Linear Algebra, Chapman and Hall, 1986.
[6] F. Botelho and J. Jamison, A learning rule with generalized Hebbian synapses, Journal Mathematical
Analysis and Applications, 273 (2002), 629-547.
[7] G. Brendon, Topology and Geometry, Graduate Texts in Mathematics, Springer Verlag, 139, 1991.
[8] J. Campos and J. Mawhin, Periodic solutions of quaternionic-valued ordinary differential equations,
Preprint (2005).
[9] S. De Leo and G. Ducati, Quaternionic differential operators, J. Math. Phys., 42 (2001),
2236-2265.
[10] S. De Leo and G. Ducati, Solving simple quaternionic differential equations, J. Math. Phys.,
44 (2003), no. 5, 2224-2233.
[11] S. De Leo and G. Scolarici, Right eigenvalue equation in quaternionic quantum mechanics, J.
Phys., Series A, 33 (2000), 2971-2995.
[12] J. Dollard and C. Friedman, Product integration with applications to differential equations,
Encyclopedia of Mathematics and its Applications, 10 (1979).
[13] F. Ham and I. Kostanic, Principles of Neurocomputing for Science and Engineering, McGraw
Hill, 2001.
[14] S. Haykin, Neural Networks: A Comprehensive Foundation, Macmillan College Publ. Co.,
1994.
[15] D. Hebb, The Organition of Behavior: A Neurophysiological Theory, Wiley, New York, 1949.
[16] J. Hertz, A. Krogh and R. Palmer, Introduction to the Theory of Neural Computation, A
Lecture Notes Volume, Santa Fe Institute Studies in the Sciences of Complexity, 1991.
[17] A. Katok and B. Hasselblatt, Introduction to modern theory of dynamical systems, Encyclopedia
of Mathematics and its Applications, 54 (1995).
[18] V. Kravchenko and B. Williams, A quaternionic generalisation of the Ricatti differential equation,
Preprint (2005).
[19] J. Kuipers, Quaternions and Rotation Sequences: A Primer with Applications to Orbits,
Aerospace, and Virtual Reality, Princeton University Press, 1999.
[20] Y. Kuznetsov, Elements of Applied Bifurcation Theory, Applied Mathematical Sciences, 112, 1998.
[21] K. Kingsley and P. Adams, Formation of new connections by a generalisation of Hebbian
learning, Preprint (2001).
[22] T. Kohonen, An introduction to neural computing, Neural Networks, 1 (1988), 3-16.
[23] P. Lancaster and M. Tismenetsky, The Theory of Matrices, Computer Science and Applied
Mathematics, Academic Press, Inc., 1985.
[24] D. Lukes, Differential equations: Classical to controlled, Mathematics in Science and Engineering, 162 (1982).
[25] N. Lloyd, The number of periodic solutions of the equation ˙z = z N + p1(t)z N−1 + · · · + pN(t) ,
Proc. London Math. Soc., 27 (1973), 667-700.
[26] V. Nemytskii and V. Stepanov, Qualitative Theory of Differential Equations, Dover Publications, Inc., 1989.
[27] E. Oja, A simplified neuron model as a principal component analyzer, J. of Math. Biology, 15
(1982), 267-273.
[28] E. Oja and J. Karhunen, A stochastic approximation of the eigenvectors and eigenvalues of
the expectation of a random matrix, J. of Math. Analysis and Appl., 106 (1985), 69-84.
[29] J. Ortega and W. Rheinboldt, Iterative Solutions of Nonlinear Equations in Several Variables,
Computer Science and Applied Mathematics, 1970.
[30] J. Ringrose, Compact Non-Self-Adjoint Operators, Van Nostrand Reinhold, 1971.
[31] L. Perko, Differential Equations and Dynamical Systems, Texts in Applied Mathematics, Springer Verlag, 7, 2000.