Periodic attractnrs aic sets of points that the system e\.utl> retraces over and ovei again and are utten referred to as limit ivtlt's. As with equilibria, a limit cycle is termed locally stable it the system approaches the cvclc as time passes for all values ot the state vauables close io the cycle. EJrnit cycles can be globally stable .is well Similarly itmtabl? limit cycles lor repelling limit nv/esj can also occur The system will remain on an unstable limit evile il it is started e\actl> on the cycle, but once perturbed olt the cycle, it will move awav. I'inalh. neutrally stable cycles, called nmtrril limit ;w/, s are also possible. The neutral cycle that a system exhibits is determined by the starting conditions; it perturbed, the system does not return to the original neutral cycle but exhibits a new neutral cycle. When there is a neutral limit cycle, infinitely manv such
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