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Dynamics of three coupled limit cycle oscillators with application to artificial intelligence

Authors:	Lee Mendelowitz Anael Verdugo Richard Rand

Institution:	1. Centro Universitario de los Lagos, Enrique Díaz de León 1144, Paseos de la Montaña, Lagos de Moreno 47460, Jalisco, Mexico;2. Center for Biomedical Technology, Technical University of Madrid, Campus Montegancedo, Pozuelo de Alarcon, Madrid 28223, Spain;3. Centro de Investigaciones en Óptica, Loma del Bosque 115, Lomas del Campestre, Leon, Guanajuato 37150, Mexico;1. Department of Mathematics and Computer Science, University of Larbi Tebessi, Tebessa, 12002, Algeria;2. Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 19117, Jordan;3. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;4. Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan;1. Department of Physics, University of Calicut, Kerala 673635, India;2. Department of Physics, Farook College, University of Calicut, Kerala 673632, India;3. Department of Physics, Tuskegee University, Tuskegee, AL 36088, US

Abstract:	We study a system of three limit cycle oscillators which exhibits two stable steady states. The system is modeled by both phase-only oscillators and by van der Pol oscillators. We obtain and compare the existence, stability and bifurcation of the steady states in these two models. This work is motivated by application to the design of a machine which can make decisions by identifying a given initial condition with its associated steady state.

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