The global behaviour of the control systems described by the pair of differential equationsx˙=−f(x)±g(y)+p(t),y˙=−f(x)±g(y)+p(t)has been investigated. Heref(x),g(y),h(x) andk(y) are polynomials of odd degree with leading coefficients positive andp(t) andq(t) are bounded functions of time. Sufficient conditions have been found under which the trajectories of the above system may eventually be confined in a subset of (x, y, t)-space, thus giving bounds on the amplitude of periodic as well as aperiodic oscillations. Further bounds on the amplitude of oscillations have been investigated by finding regions in (x,y,t)-space from which all trajectories eventually leave and into which no trajectories enter. Thus sufficient conditions have been derived for the existence of an annulus in which oscillatory behaviour may be c
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