It is rigorously proven under certain assumptions that a quasilinear system with discontinuous right-hand side possesses a unique unpredictable solution. The discontinuous perturbation function on the right-hand side is defined by means of an unpredictable sequence. A Gronwall-Coppel type inequality is utilized to achieve the main result, and the stability of the unpredictable solution is discussed. Examples with exponentially asymptotically stable and unstable unpredictable solutions are provided.
Unpredictable solution, unpredictable sequence, quasilinear system, Poincare chaos, discontinuous right-hand side
FEN, MEHMET ONUR and FEN, FATMA
"Quasilinear systems with unpredictable relay perturbations,"
Turkish Journal of Mathematics: Vol. 46:
4, Article 19.
Available at: https://journals.tubitak.gov.tr/math/vol46/iss4/19