This book provides new research on the advances in nonlinear dynamics. Chapter One studies compactons in carbon nanotube arrays. Chapter Two reviews the elastic and plastic type behaviors in the Fractal Theory of Motion at nanoscale. Chapter Three analyzes a particular model of tumor 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 behaviors of traveling waves and Shapiro step types in a tumor-growth model. Chapter Seven discusses the astonishing evolutionary dynamics of a class of nonlinear discrete 2D pattern formations and growth models.
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