This book provides new research on the advances in non-linear dynamics. Chapter One studies compactions in carbon nanotube arrays. Chapter Two reviews the elastic and plastic type behaviours in the Fractal Theory of Motion at nanoscale. Chapter Three analyses a particular model of tumour progression, assuming that the invasive cells, the connective tissue and the proteases are moving through a non-differential medium governed by the Non-Standard Scale Relativity Theory (NSRT) (Scale Relativity Theory with arbitrary constant fractal dimension). Chapter Four studies the process of drug release from a polymer matrix. Chapter Five examines the implications of drug release from a polymeric matrix process. Chapter Six reviews behaviours of travelling waves and Shapiro step types in a tumour-growth model. Chapter Seven discusses the astonishing evolutionary dynamics of a class of nonlinear discrete 2D pattern formations and growth models.