This paper presents analysis of Lyapunov type stability for multiplicative dynamical systems. It has been formally defined and numerical simulations were performed to explore nonlinear dynamics. Chaotic behavior manifested for exemplary multiplicative dynamical systems has been confirmed by calculated Lyapunov exponent values.
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Aniszewska, D., Rybaczuk, M. Lyapunov type stability and Lyapunov exponent for exemplary multiplicative dynamical systems. Nonlinear Dyn 54, 345–354 (2008). https://doi.org/10.1007/s11071-008-9333-7