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This article studies the problem of reachable set bounding for the discrete-time nonlinear positive systems with time-varying delay and disturbance for the first time. Discrete-time nonlinear positive systems whose vector fields are homogeneous of degree greater than one and order preserving are discussed. By using a novel technique which does not involve the Lyapunov-Krasovskii functional approach, necessary and sufficient criteria are established to guarantee all the state trajectories of the system converge exponentially within a special ball.Moreover, we extend the main results to general nonlinear time-varying systems with disturbance. Finally, numerical examples well show the superiority of the obtained results.

This paper examines the Turing patterns and the spatio-temporal chaos of non-autonomous systems defined on hypergraphs. The analytical conditions for Turing instability (TI) and Benjamin-Feir instability (BFI) are obtained by linear stability analysis using new comparison principles. The comparison with pairwise interactions is presented to reveal the effect of higher-order interactions on pattern formation. In addition, numerical simulations due to different non-autonomous mechanisms, such as time-varying diffusion coefficients, time-varying reaction kinetics and time-varying diffusion coupling are provided respectively, which verifies the efficiency of theoretical results.