We consider a Nicholson’s equation with multiple pairs of time-varying delays and nonlinear terms given by mixed monotone functions. Sufficient conditions for the permanence, local stability and global attractivity of its positive equilibrium K are established. The main novelty here is the construction of a suitable auxiliary difference equation x n+1 = h(x n ) with h having negative Schwarzian derivative, and its application to derive the attractivity of K for a model with one or more pairs of time-dependent delays. Our criteria depend on the size of some delays, improve results in recent literature and provide answers to open problems.

We study the competitive irreversible adsorption of a binary mixture of monomers and square-shaped particles of linear size R on the square lattice. With the random sequential adsorption model, we investigate how the jamming coverage and percolation properties depend on the size ratio R and relative flux F. We find that the onset of percolation of monomers is always lower for the binary mixture than in the case with only monomers (R = 1). Moreover, for values F below a critical value, the higher is the flux or size of the largest species, the lower is the value of the percolation threshold for monomers.

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