Abstract
In this paper, spreading properties of reaction-diffusion systems with cooperative and reducible nonlinearity are considered. Weinberger et al. [J. Math. Biol.
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(2002) 183-218] demonstrated that components of reducible cooperative systems can spread at distinct finite speeds for given compactly supported initial conditions. We extend this analysis by considering the possible acceleration spreading. Our findings reveal that all components can propagate at different speeds, either linearly or superlinearly (acceleration). By employing the graph theory, we specifically characterize the level sets of solutions, illustrating the influence of the cooperative effect. Examples are presented to illustrate the obtained results.