Series Preface * Preface to the Third Edition * 1 Linear Systems * 2 Nonlinear Systems: Local Theory * 3 Nonlinear Systems: Global Theory * 4 Nonlinear Systems: Bifurcation Theory * References * Index

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Differential Equations and Dynamical Systems

Part One: One-Dimensional Dynamics Examples of Dynamical Systems Preliminaries from Calculus Elementary Definitions Hyperbolicity An example: the quadratic family An Example: the Quadratic Family Symbolic Dynamics Topological Conjugacy Chaos Structural Stability Sarlovskiis Theorem The Schwarzian Derivative Bifurcation Theory Another View of Period Three Maps of the Circle Morse-Smale Diffeomorphisms Homoclinic Points and Bifurcations The Period-Doubling Route to Chaos The Kneeding Theory Geneaology of Periodic Units Part Two: Higher Dimensional Dynamics Preliminaries from Linear Algebra and Advanced Calculus The Dynamics of Linear Maps: Two and Three Dimensions The Horseshoe Map Hyperbolic Toral Automorphisms Hyperbolicm Toral Automorphisms Attractors The Stable and Unstable Manifold Theorem Global Results and Hyperbolic Sets The Hopf Bifurcation The Hnon Map Part Three: Complex Analytic Dynamics Preliminaries from Complex Analysis Quadratic Maps Revisited Normal Families and Exceptional Points Periodic Points The Julia Set The Geometry of Julia Sets Neutral Periodic Points The Mandelbrot Set An Example: the Exponential Function

An introduction to chaotic dynamical systems (2nd edition), by Robert L. Devaney. Pp 336. £34·95. 1989. ISBN 0-201-13046-7 (Addison-Wesley)

The application of a memristor in chaotic circuits is increasingly becoming a popular research topic. The influence of a memristor on the dynamics of chaotic systems is worthy of further exploration. In this paper, a multi-dimensional closed-loop coupling model based on a Logistic map and Sine map (CLS) is proposed. The new chaotic model is constructed by cascade operation in which the output of the Logistic map is used as the input of the Sine map. Additionally, the one-dimensional map is extended to any dimension through the coupling modulation. In order to further increase the complexity and stability of CLS, the discrete memristor model is introduced to construct a discrete memristor-based coupling model with a Logistic map and a Sine map (MCLS). By analyzing the Lyapunov exponents, bifurcation diagram, complexity, and the 0–1 test result, the comparison result between CLS and MCLS is obtained. The dynamics performance analysis shows that the Lyapunov exponents and bifurcation diagrams present symmetrical distribution with variations of some parameters. The MCLS has parameters whose values can be set in a wider range and can generate more complex and more stable chaotic sequences. It proves that the proposed discrete memristor-based closed-loop coupling model can produce any higher dimension hyperchaotic system and the discrete memristor model can effectively improve the performance of discrete chaotic map and make this hyperchaotic system more stable.

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Design of a New Dimension-Changeable Hyperchaotic Model Based on Discrete Memristor

New solutions for chirped optical solitons related to Kaup-Newell equation: Application to plasma physics

th , 2012 ABSTRACT: Friction and wear coefficient represent two important variables for hard coating selection in critical engineering applications such as cutting and material forming. To explain fully these variables, is necessary to understand different types of wear mechanisms that occur in coated surfaces. Zirconium nitride (ZrN), chromium nitride (CrN) and titanium aluminum nitride (TiAlN) coatings produced by reactive magnetron sputtering technique were evaluated. The tribological properties- coefficient of friction (COF) and wear coefficient were investigated using a ball on disc tribometer and profilometry. Bias polarization voltage showed an increase in plastic deformation and third body generation failures in the ZrN surface. Nitrogen flux increasing in CrN deposition, improves tribological behavior due to cubic phase segregation, enhancing superficial properties. Increasing substrate temperature during deposition of TiAlN improves superficial properties (roughness and porous density decrease), increases abrasion wear resistance and load capability of the coating.

TRIBOLOGY OF ZrN, CrN AND TiAlN THIN FILMS DEPOSITED BY REACTIVE MAGNETRON SPUTTERING TRIBOLOGÍA DE RECUBRIMIENTOS DE ZrN, CrN Y TiAlN OBTENIDOS POR MAGNETRON SPUTTERING REACTIVO

The nonlinear differential equation governing the periodic motion of the one-dimensional, undamped, and unforced cubic-quintic Duffing oscillator is solved exactly, providing exact expressions for the period and the solution. The period as well as the exact analytic solution is given in terms of the famous Weierstrass elliptic function. An integrable case of a damped cubic-quintic equation is presented. Mathematica code for solving both cubic and cubic-quintic Duffing equations is given in Appendix at the end.

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A New Approach for Solving the Complex Cubic-Quintic Duffing Oscillator Equation for Given Arbitrary Initial Conditions

In this paper, we present an analytical, numerical, and experimental description of the period addition phenomenon in a dynamical system arising from a boost converter controlled by ZAD strategy. T...

Period Addition Phenomenon and Chaos Control in a ZAD Controlled Boost Converter

En este articulo se presentan algunas caracteristicas estructurales y quimicas de materiales utilizados comunmente en aplicaciones industriales como nitruro de titanio (TiN) y carburo de titanio (TiC). El analisis inicial se llevo a cabo a partir de los diagramas de fase del TiN y el TiC. En ellos se observan propiedades importantes como punto de fusion, punto de evaporacion, polimorfismo y solubilidad entre otros. La comprension de estos diagramas de fase lleva a un mejor entendimiento de las caracteristicas de estos materiales. Por otro lado se hizo una evaluacion de los enlaces quimicos que resultan en la formacion de las moleculas del TiN y TiC, teniendo en cuenta que en estos compuestos se presenta una combinacion de enlaces ionico, covalente y metalico, lo que les otorga excelentes propiedades electricas mecanicas y tribologicas. Ademas, se considero la hibridacion que se produce para conseguir compuestos estables.

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Algunos conceptos sobre nitruro de titanio y el carburo de titanio

In this work a sumary of structural and chemical characteristics of materials commonly employed in industrial applications such as TiN and TiC was realized. The analysis was realized from the phase diagrams of TiN and TiC. This materials present, important characteristics such as melting point, boiling point, polymorphism and solubility among others, are observed. These phase diagrams carry to a best understanding to the material properties. On the other hand, an analysis of chemical bonds that result in the TiN and TiC molecules formation, having into a count that they present ionic, covalent and metallic molecular combination bonds was carried out. Moreover, the hybridization that is produced in order to get stable compounds was considered.

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Algunos conceptos sobre nitruro de titanio y el carburo de titanio some concepts about titanium nitride and titanium carbide

This paper analyzes the dynamics of a system that models the formation of biofilms in a continuous stirred-tank reactor (CSTR) when it is utilized for wastewater treatment The growth rate of the microorganisms is modeled using two different kinetics, Monod and Haldane kinetics, with the goal of studying the influence of each in the system The equilibrium points are identified through a stability analysis, and the bifurcations found are characterized

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Simeón Casanova Trujillo

Papers

A New Approach for Solving the Complex Cubic-Quintic Duffing Oscillator Equation for Given Arbitrary Initial Conditions

Period Addition Phenomenon and Chaos Control in a ZAD Controlled Boost Converter

Algunos conceptos sobre nitruro de titanio y el carburo de titanio

Algunos conceptos sobre nitruro de titanio y el carburo de titanio some concepts about titanium nitride and titanium carbide

Dynamical Analysis of a Continuous Stirred-Tank Reactor with the Formation of Biofilms for Wastewater Treatment