<p>A novel mechanism of non-classical excitation in the asymptotic states of a linear dynamical system is presented. Based on an intrinsically devised nonlinear iteration on a scale invariant linear first order differential equation in the Complex plane, the standard linear response (map) is shown to undergo local continuous deformations having a filled Julia set type limit set of a quadratic map. Because of scale invariance, this local deformation can be extended globally, converting the original linear system output into a nonlinear one. A neural network interpretation of this construction reveals its potential applications in biological and other complex systems. An extension of neural network architecture is considered incorporating ’intelligent neurons’, that can be invoked to enable non-classical excitation in a general neural network. An application of this proposal is discussed in a soliton model of artery blood flow dynamics and in management of human health.</p>