On Computing Coupled Turning Points of Parameter Dependent Nonlinear Equations

Abstract

Let us given an n-dimensional nonlinear system

$$F\left( {x,p} \right) = 0$$

(1.1a)

that expresses implicitly the relation between the state variables x∈ℝⁿ⁺¹ and a selected design parameter p∈ℝ¹. In general, the system (1.1a) describes a real process that depends on some auxiliary parameters. In this paper we consider only one design parameter p. Moreover, one variable of the vector x∈ℝⁿ⁺¹, say the (n+1)−th component x _n+1, is easily controllable and plays the role of the unfolding parameter.