Strong and weak oscillatory behavior in time-varying linear difference equations of arbitrary order in the presence of unmodeled dynamics and nominal parametrical errors

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This paper is devoted to investigate the presence of oscillating solutions in time-varying difference equations of arbitrary nth order even in the case when there are parametrical errors (i.e. errors in the sequences defining their coefficients) or unmodeled dynamics (i.e. the current order n is unknown with n > n 0 – the nominal known order). The problem is formulated linked to the concepts of conjugacy, disconjugacy, positivity and generalized zeros and very general conditions of oscillation are obtained both over particular intervals and for the whole solution. Some results concerned with the presence of stable/asymptotically stable oscillatory solutions are also presented.