Discrete Dynamical Systems and Difference Equations with Mathematica

By Mustafa R. S. Kulenovic, O. Merino. 2002

263 citations recorded by the source corpus.

DYNAMICS OF ONE-DIMENSIONAL DYNAMICAL SYSTEMS Introduction Linear Difference Equations with Constant Coefficients Linear Difference Equations with Variable Coefficients Stability Stability in the Non-Hyperbolic Case Bifurcations Dynamica Session Symbolic Dynamics for One-Dimensional Maps Dissipative Maps and Global Attractivity Parametrisation and Poincare Functional Equation Exercises DYNAMICS OF TWO-DIMENSIONAL DYNAMICAL SYSTEMS Introduction Linear Theory Equilibrium Solutions The Riccati Equation Linearized Stability Analysis Dynamica Session Period Doubling Bifurcation Lyapunov Numbers Box Dimension Semicycle Analysis Stable and Unstable Manifold Dynamica Session on Henon's Equation Invariants Lyapunov Functions, Stability, and Invariants Dynamica Session on Lyness' Map Dissipative Maps and Systems Dynamica Session on Rational Difference Equations Area-preserving Maps and Systems Biology Applications Projects Applications in Economics Exercises SYSTEMS OF DIFFERENCE EQUATIONS, STABILITY, AND SEMICYCLES Introduction Linear Theory Stability of Linear Systems The Routh-Hurwitz and Schur-Cohn Criterion Nonlinear Systems and Stability Limit Sets and Invariant Manifolds Dissipative Maps Stability of Difference Equations Semicycle Analysis Dynamica Session on Semicycles Exercises INVARIANTS AND RELATED LYAPUNOV FUNCTIONS Introduction Invariants for Linear Equations and Systems Invariants and Corresponding Lyapunov Functions for Nonlinear Systems Invariants of Special Class of Difference Equations Applications Dynamica Session on Invariants Dynamica Session on Lyapunov Functions Invariance under Lie Group Transformations Exercises DYNAMICS OF THREE-DIMENSIONAL DYNAMICAL SYSTEMS Introduction Dynamica Session on Third Order Difference Equations Dissipative Difference Equation of Third Order Dynamica Session on Local Asymptotic Stability of Period-Two Solution Dynamica Session on Todd's Difference Equation Biology Applications Projects Exercises FRACTALS GENERATED BY ITERATED FUNCTIONS SYSTEMS Introduction Basic Definitions and Results Iterated Function System Basic Results on Iterated Functions Systems Calculation of Box Dimension for IFS Dynamica Session Exercises BIBLIOGRAPHY INDEX

Subfields: Public Health, Environmental and Occupational Health

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Citations in the corpus

Global asymptotic stability of a system of difference equations (2008, background): “Here, we review some results [5] which will be useful in our investigation of the behaviour of solutions of the system (3).”
On a System of Rational Difference Equations (2010, background): “Here, we review some results [6] which will be useful in our investigation of the behavior of the solutions of the system (1).”
On a k-Order System of Lyness-Type Difference Equations (2007, background): “So there exist many papers concerning systems of difference equations (see [1–10] and the references cited therein).”
Asymptotic behavior of a competitive system of linear fractional difference equations (2006, background): “Here (S) denotes the basin of attraction of a set S, see [4, 10, 15].”
Dynamics of a two-dimensional system of rational difference equations of Leslie--Gower type (2011, background): “Competitive and cooperative systems have been investigated by many authors, see [2,3,5-19].”