Bifurcation control and chaos in a linear impulsive system

Bifurcation control and the existence of chaos in a class oflinear impulsive systems are discussed by means of both theoreticaland numerical ways. Chaotic behaviour in the sense of Marotto'sdefinition is rigorously proven. A linear impulsive controller,which does not result in any change in one period-1 solution of theoriginal system, is proposed to control and anti-control chaos. Thenumerical results for chaotic attractor, route leading to chaos,chaos control, and chaos anti-control, which are illustrated withtwo examples, are in good agreement with the theoretical analysis.