**Meet the editor**

Ricardo López-Ruiz, MS, PhD, works as an associate professor in the Department of Computer Science and Systems Engineering, Faculty of Science, University of Zaragoza, Spain. He also serves as an associate researcher in Complex Systems at the School of Mathematics, University of Zaragoza. He also worked as a lecturer in the University of Navarra, the Public University of

Navarra, and the UNED of Calatayud. He completed his postdoc with Prof. Yves Pomeau at the École Normale Supérieure of Paris and with Prof. Gabriel Mindlin at the University of Buenos Aires. His areas of interest include statistical complexity and nonlinear models, chaotic maps and applications, multiagent systems, and econophysics.

Contents

**Preface VII**

**Chemostat 45**

**Section 1 Complexity in Biological Systems 1**

Chapter 1 **Mechanical Models of Microtubules 3** Slobodan Zdravković

Chapter 2 **The Dynamics Analysis of Two Delayed Epidemic Spreading**

Chapter 3 **Stability and Hopf Bifurcation Analysis of a Simple Nutrient-Prey-Predator Model with Intratrophic Predation in**

Chapter 4 **Sensitivity Analysis: A Useful Tool for Bifurcation Analysis 69**

Chapter 5 **Biological Hypercomputation and Degrees of Freedom 83**

Qiming Liu, Meici Sun and Shihua Zhang

Zabidin Salleh and Liyana Abd Rahim

Raheem Gul and Stefan Bernhard

Chapter 6 **Self-Organization, Coherence and Turbulence in**

Vladimir L. Kalashnikov and Evgeni Sorokin

Chapter 7 **Interaction of Solitons with the Electromagnetic Field in Classical Nonlinear Field Models 113**

Carlos Eduardo Maldonado

**Section 2 Complexity in Physical Systems 95**

**Laser Optics 97**

Jon C. Luke

**Models with Latent Period on Heterogeneous Network 25**

## Contents

#### **Preface XI**


Chapter 8 **A Perturbation Theory for Nonintegrable Equations with Small Dispersion 133** Georgy Omel'yanov

Preface

scientists, and postgraduate students.

ten in this dedicatory final paragraph.

Modeling and simulating biological and physical systems are nowadays active branches of sci‐ ence. The diversity and complexity of behaviors and patterns present in the natural world have their reciprocity in the life systems. Bifurcations, solitons and fractals are some of these ubiqui‐ tous structures that can be indistinctively identified in many models with the most diverse appli‐ cations, from microtubules with an essential role in the maintenance and the shaping of cells, to the nano/microscale structure in disordered systems determined with small-angle scattering techniques. This book collects several works in this direction, giving an overview of some mod‐ els and theories that are useful for the study and analysis of complex biological and physical systems. It can provide a good guidance for physicists with interest in biology, applied research

The first section of the book presents different biological models with a wide variety of applica‐ tions. In Chapter 1, Zdravkovic presents three nonlinear mechanical models to explain the dy‐ namics of solitons in microtubules. In Chapter 2, Liu et al. study the behavior of two delayed epidemic spreading models on scale-free networks. In Chapter 3, Salleh and Rahim investigate the existence and stability of equilibria in a nutrient-prey-predator model with intratrophic pre‐ dation. In Chapter 4, Gul and Bernhard apply global sensitivity analysis to a multicompartment, lumped-parameter model of an arm artery to identify the bifurcation parameters of the arm ar‐ teries. The last chapter of this section, Chapter 5 by Maldonado, introduces the idea of biological hypercomputation and analyzes the relationship between matter, energy and information.

The second section of the book presents some physical models showing soliton and fractal behav‐ iors. In Chapter 6, Kalashnikov and Sorokin present the concept of dissipative soliton and its full life cycle as a self-organized object. In Chapter 7, Luke discusses the use of solitons for particle models in the nonlinear Klein-Gordon equation. In Chapter 8, Omel'yanov considers the problem of propagation and interaction of solitons in the generalized KdV equation. In Chapter 9, Noreldin at al. perform a weakly nonlinear stability analysis of the flow of a nanofluid in a porous medium with stress-free boundary conditions. Finally, in the last chapter, Chapter 10, Anitas introduces the concepts of mass and surface fractals in the context of small-angle scattering techniques.

As the editor of this book, I would like to thank all the authors who have contributed to this volume as well as the reviewers for their assessment. Also, I must express my gratitude to the InTechOpen editorial staff for their invitation asking me to be the editor for the second time. With particular help from Ms. Kristina Kardum, the Publishing Process Manager (PPM), we have arrived to convert in this new InTechOpen book. Finally, at this moment where life is a nonsense time flow, I want to dedicate all this effort to the memory of my father, Ricardo López-Barasoain (1935–2015), and to my mother, Amelia Ruiz-Gastón (1935–present), from Villafranca, Navarra, Spain. Of course, the rest of my family and all my friends and advisers are not forgot‐

**Ricardo López-Ruiz**

University of Zaragoza, Spain

