| Abstract: |
| Delay equations are increasingly used in mathematical models for biological systems. Populations with age or size structure, for instance, can be described with a renewal equation for the population birth rate, possibly coupled with a delay differential equation for the environmental variable. But no software is capable of studying numerically the bifurcation properties of this kind of nonlinear systems. To address this gap, we propose the pseudospectral discretization technique as a way to approximate a general nonlinear delay equation with a low-dimensional system of ordinary differential equations, whose properties can be studied with existing software. The technique can be applied to systems coupling both renewal and delay differential equations, and involving bounded or unbounded delays. Using some numerical examples, we explore the effectiveness and flexibility of the method. |
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