Research

On the basis of studies of the olfactory bulb of a rabbit Freeman suggested that in the rest state the dynamics of this neural cluster is chaotic, but that when a familiar scent is presented the neural system rapidly simplifies its behaviour and the dynamics becomes more orderly, more nearly periodic than when in the rest state. This suggests an interesting model of recognition in biological neural systems. To realize this in an artificial neural system, some form of control of the chaotic neural behaviour is necessary to achieve periodic dynamical behaviour when a stimulus is presented.

We first study the general problem of modelling smooth systems and introduce a number of useful techniques relevant to the problem of modelling chaotic dynamics. After a preliminary review of chaotic dynamical systems and their control, and discussing several examples of neural chaos, we then construct a chaotic neural model. We show how this model can be successfully controlled using several different parametric control methods. However, such methods of control are external to the network and we are interested in the control of higher dimensional networks using a technique which is intrinsic to the neural dynamics.

Using a higher dimensional system we investigate several methods of control and conclude that control using delayed feedback is a feasible mechanism for producing the retrieval behaviour described by Freeman. Delayed feedback provides a mechanism for stabilization onto unstable periodic behaviours. The particular unstable periodic orbit which is stabilized depends quite strongly on the precise character of the applied stimulus. Thus the system can act as an associative memory in which the act of recognition corresponds to stabilizing onto an unstable periodic orbit which is characteristic of the applied stimulus. The entire artificial system therefore exhibits an overall behaviour and response to stimulus which precisely parallels the biological neural behaviour observed by Freeman.

Parameter choices for control of a chaotic neural network, Alban P.M. Tsui and Antonia J. Jones. Advances in Intelligent Systems, Ed. F.C. Morabito, Frontiers in Artificial Intelligence and Applications 41, IOS Press, University of Reggio Calabria, Italy, Sepetember, 1997, Pages 118-123.
Using a neural network to calculate the sensitivity vectors in synchronisation of chaotic maps, Ana Guedes de Oliveira, Alban Pui Man Tsui and Antonia J. Jones, Proceedings 1997 International Symposium on Nonlinear Theory and its Applications (NOLTA'97) 1, Research Society of Nonlinear Theory and its Applications, IEICE, Honolulu, U.S.A., Nov.29--Dec.2, Pages 105-108.
Periodic Response to External Stimulation of a Chaotic Neural Network with Delayed Feedback, Alban P.M. Tsui and Antonia J. Jones, International Journal of Bifurcation and Chaos, 9(4):713-722, 1999. Abstract and some info.
The control of higher dimensional chaos: comparative results for the chaotic satellite attitude control problem, Alban P.M. Tsui and Antonia J. Jones. To appear in Physica D 135(1-2):41-62, Nov 1999, Abstract and some interactive info here.

A scenery outside the secret research farm.
Thesis title: Smooth Data Modelling and Stimulus-Response System via Neural Chaos
Alban Pui Man Tsui PhD in Computing from Department of Computing, Imperial College, London, University of London. MSc in Information Processing and Neural Networks, Kings College London, University of London. BSc in Mathematics and Computer Science, Kings College London, University of London. Supervised by Prof. Antonia J. Jones Deparment of Computer Science, University of Wales, Cardiff, U.K.
Thesis Abstract On the basis of studies of the olfactory bulb of a rabbit Freeman suggested that in the rest state the dynamics of this neural cluster is chaotic, but that when a familiar scent is presented the neural system rapidly simplifies its behaviour and the dynamics becomes more orderly, more nearly periodic than when in the rest state. This suggests an interesting model of recognition in biological neural systems. To realize this in an artificial neural system, some form of control of the chaotic neural behaviour is necessary to achieve periodic dynamical behaviour when a stimulus is presented. We first study the general problem of modelling smooth systems and introduce a number of useful techniques relevant to the problem of modelling chaotic dynamics. After a preliminary review of chaotic dynamical systems and their control, and discussing several examples of neural chaos, we then construct a chaotic neural model. We show how this model can be successfully controlled using several different parametric control methods. However, such methods of control are external to the network and we are interested in the control of higher dimensional networks using a technique which is intrinsic to the neural dynamics. Using a higher dimensional system we investigate several methods of control and conclude that control using delayed feedback is a feasible mechanism for producing the retrieval behaviour described by Freeman. Delayed feedback provides a mechanism for stabilization onto unstable periodic behaviours. The particular unstable periodic orbit which is stabilized depends quite strongly on the precise character of the applied stimulus. Thus the system can act as an associative memory in which the act of recognition corresponds to stabilizing onto an unstable periodic orbit which is characteristic of the applied stimulus. The entire artificial system therefore exhibits an overall behaviour and response to stimulus which precisely parallels the biological neural behaviour observed by Freeman. Publications (available in acrobat PDF) Parameter choices for control of a chaotic neural network, Alban P.M. Tsui and Antonia J. Jones. Advances in Intelligent Systems, Ed. F.C. Morabito, Frontiers in Artificial Intelligence and Applications 41, IOS Press, University of Reggio Calabria, Italy, Sepetember, 1997, Pages 118-123. Using a neural network to calculate the sensitivity vectors in synchronisation of chaotic maps, Ana Guedes de Oliveira, Alban Pui Man Tsui and Antonia J. Jones, Proceedings 1997 International Symposium on Nonlinear Theory and its Applications (NOLTA'97) 1, Research Society of Nonlinear Theory and its Applications, IEICE, Honolulu, U.S.A., Nov.29--Dec.2, Pages 105-108. Periodic Response to External Stimulation of a Chaotic Neural Network with Delayed Feedback, Alban P.M. Tsui and Antonia J. Jones, International Journal of Bifurcation and Chaos, 9(4):713-722, 1999. Abstract and some info. The control of higher dimensional chaos: comparative results for the chaotic satellite attitude control problem, Alban P.M. Tsui and Antonia J. Jones. To appear in Physica D 135(1-2):41-62, Nov 1999, Abstract and some interactive info here. Some of the publications including my thesis, in pdf form, are available here. Research Interests Chaos control Neural Networks Computational Geometry Another scenery behind the secret research farm.