Construction of multiple trade-offs to obtain arbitrary singularities of adaptive dynamics (Q2339109)

The aim of the paper is for a given strategy \(x\) with arbitrary trait vector \(f(x)\) to find vectors \(f'(x)\) and \(f''(x)\) such that if \[ f(y)=f(x)+f'(x)(y-x)+f''(x)(y-x)^2+O((y-x)^3) \] then \(x\) is a singularity of a given type (for example, \(x\) is an evolutionary branching point). As an application, the author considers a model of ecological dynamics given by a system of four ordinary differential equations.