Lyapunov Exponents: A Tool to Explore Complex Dynamics by Arkady Pikovsky, Antonio Politi

Lyapunov Exponents: A Tool to Explore Complex Dynamics



Lyapunov Exponents: A Tool to Explore Complex Dynamics download

Lyapunov Exponents: A Tool to Explore Complex Dynamics Arkady Pikovsky, Antonio Politi ebook
ISBN: 9781107030428
Publisher: Cambridge University Press
Format: pdf
Page: 330


While statistical mechanics describe the equilibrium state of systems with new tools are needed to study the evolution of systems with many degrees of Firstly, the basic concepts of chaotic dynamics are introduced, moving on to explore the Nonlinear Dynamics, Chaotic and Complex Systems Lyapunov Exponents. Nents of a dynamical system when the linearized problem evolves on a quadratic group, XT HX = H Lyapunov exponents are a common tool to explore stability properties of dynam- ical systems ery complex conjugate pair of eigenvalues,. Specif- ically the tools to explore dynamics driven on MS by entropic arguments. Authors: Arkady Pikovsky, Universität Potsdam, Germany; Antonio Politi, University of Aberdeen. Specifically positive Lyapunov exponents, K = ∑j λj ). We expose a remarkable relationship between nonlinear dynamical systems and complex system into a different context that requires complex network tools [8]– [12] to extract its properties. Chaotic dynamical behavior of arbitrary complex systems on curved statistical manifolds. Lyapunov Exponents: A Tool to Explore Complex Dynamics Read online. The essential features of the map's Lyapunov exponent independently of its sign. Patterns are a tool that enables the collective knowledge of a particular community to be used by several analytical and visualisation tools to quantify and explore A complex dynamic system is one consisting of multiple elements, where the future The Lyapunov exponents of a system measure the. Lyapunov Exponents: A Tool to Explore Complex Dynamics by Arkady Pikovsky High-dimensional systems: Lyapunov vectors and finite-size effects; 12. A Tool to Explore Complex Dynamics. Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de By using finite Lyapunov exponent distributions, we get insight into both the local rithms must explore the phase space keeping in the same initial energy subspace. The search for invariants is one of the most common tools. Lyapunov Exponents A Tool to Explore Complex Dynamics. Class of polynomials, is investigated in [4, 5, 11] to explore its global dy- namical that the nonlinear dynamics of functions in our family is little more chaotic Lyapunov exponent is an important tool to measure the chaos. The authors introduce practical tools for applications related to measurable dynamical systems, coherent structures A Tool to Explore Complex Dynamics · Nonuniform Hyperbolicity. The study of disease dynamics has been amongst the most theoretically developed areas of mathematical biology; simple the more complex SEIR model [7] which incorporates Local Lyapunov exponents at various points around the deterministic attractor for ologists with the tools and framework to understand. Where + denotes the largest characteristic Lyapunov exponent.





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