Determining the flexibility of regular and chaotic attractors

We present an overview of measures that are appropriate for determining the flexibility of regular and chaotic attractors. In particular, we focus on those system properties that constitute its responses to external perturbations. We deploy a systematic approach, first introducing the simplest measure given by the local divergence of the system along the attractor, and then develop more rigorous mathematical tools for estimating the flexibility of the system’s dynamics. The presented measures are tested on the regular Brusselator and chaotic Hindmarsh–Rose model of an excitable neuron with equal success, thus indicating the overall effectiveness and wide applicability range of the proposed theory. Since responses of dynamical systems to external signals are crucial in several scientific disciplines, and especially in natural sciences, we discuss several important aspects and biological implications of obtained results.