|Speaker:||Mark L. Spano, White Oak Laboratory, Naval Surface Warfare Center|
|Topic:||“Thoughts on Chaos”|
The President, Ms. Enig, called the 2032nd meeting to order at 8:19 p.m. on October 14, 1994. The Recording Secretary read the minutes of the 2031st meeting and they were approved. The President then read a portion of the minutes from the 423rd meeting, May 26, 1894.
The President introduced Mr. Mark Spano who presented some of his “Thoughts on Chaos”.
Chaos is the name given to the behavior of some wildly unpredictable systems that had remained largely unstudied until 20 years ago. With the mathematical description of chaotic systems and the successful application of methods for the control of physical chaotic systems, there has been an increased interest in chaotic biological systems, especially the heart and the brain.
What is chaos? The Greeks regarded Chaos as the primordial origin of the cosmos and the Roman Ovid in “Metamorphoses” described Chaos as a “rough unordered mass of things”. Carl Jung said “In all chaos there is a cosmos, in all disorder a secret order.” Henri Poincaire first defined chaotic systems as those in which small differences in initial conditions are sufficient to produce large and divergent differences in final phenomena. A chaotic system is exquisitely sensitive to changes in initial conditions. The chaotic changes in the measured properties of these systems is deterministic, not random, because they arise from a number of unstable periodic motions. Mathematical analysis reveals that the effects of small initial disturbances grow exponentially. This property implies that long term prediction of truly chaotic systems is impossible. However, it also implies that control of such systems is not impossible. The properties which make chaos unpredictable also make it controllable.
Many physical chaotic systems have been described mathematically including mechanical and fluid systems, planetary orbits, electrical circuits, reacting chemical mixtures, biological tissues, the spread of diseases and predator- prey populations. With a mathematical description of a system it becomes possible to distinguish those that are chaotic from those that are irregular periodic and from those that are truly random.
In 1990 three researchers at the University of Maryland devised a theory for controlling chaotic systems . Every chaotic system exhibits “fixed points”, those values around which the system's measured phenomena tend to oscillate. These “fixed points” are mathematically saddle points with at least one stable and one unstable dimension. The object of this study was to attempt to control a chaotic system by either moving the position of the saddle points or by changing the shape of the saddle point. Their methods for chaos control were successfully applied in one case to increase the output of a laser by a factor of 15 in a system with 9 unstable and 1 stable dimension.
The first successful application of these methods in controlling a chaotic biological system was in cardiology . An apparently regular heart beat is actually the product of the nearly simultaneous firing of a number of self- stimulating nerve cells in the heart. The drug oubain can be used to produce one type of abnormal behavior with the nerve cells firing together but at chaotic intervals. Small electric shocks can be used in this system to stimulate the nerves and accelerate a beat, but there is no way to retard it. Electroshock paddles cannot provide control, only a kick that may also leave the nerve cells firing independently and at random. Regularly paced electrical stimulation, such as that provided by pacemakers, can also make the problem worse by introducing another periodic signal that is not synchronized with any natural signal. It was demonstrated that even with influence exerted in only one direction, in this case advancing, of the control dimension it was nonetheless possible to achieve control of the nerve firing interval.
Recently these control methods have been applied in another chaotic biological system, epileptic seizures in the brain . While there are some drugs that can be used effectively to limit seizures, those drugs are not benign. Epileptic seizures are characterized by entrained discharges referred to as interictal spikes from foci of cells in the hippocampus. Using convulsant drug-treated hippocampal slices that exhibited similar behavior, it was shown that the intervals between successive spikes are chaotic with one stable and one unstable dimension. Chaotic control methods employing electrodes were used to make the spiking more regular. Regular spiking is not necessarily desirable, since the normal brain exhibits essentially random firing from the nerve cells. The same control methods were also used to exert anti-control making the spiking more irregular, changing it from chaotic to random. Such anti-control methods may be useful in attempting to control epilepsy.
 E. Ott, C. Grebogi, and J.A. Yorke, Phys. Rev. Lett. 64, 1196-1199, 1990.
 A. Garfinkel, M. Spano, W.L. Ditto, and J. Weiss, Science 257, 1230-1235, 1992.
 S.J. Schiff, J. Kristin, D.H. Duong, T. Chang, M.L. Spano, and W.L. Ditto, Nature 370, 615-620, 1994.
The President thanked the speaker on behalf of the Society. The incoming President on behalf of the membership chairman presented one new member. The President announced the speaker for the next meeting, made the parking announcement, and adjourned the 2032nd meeting at 9:47 p.m.
|John S. Garavelli|
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