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Ordinary Differential Equations: Dynamical Systems
2007Ordinary differential equations (ode) are differential equations for functions which depend on one independent variable only. These ‘odes’ are simpler than partial differential equations which contain more than one independent variable. In almost all models or simulations independent variables are either time and/or space.
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Differential–Algebraic Equations and Dynamic Systems on Manifolds
Cybernetics and Systems Analysis, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kryvonos, Iu. G. +2 more
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Delay differential systems for tick population dynamics
Journal of Mathematical Biology, 2014Ticks play a critical role as vectors in the transmission and spread of Lyme disease, an emerging infectious disease which can cause severe illness in humans or animals. To understand the transmission dynamics of Lyme disease and other tick-borne diseases, it is necessary to investigate the population dynamics of ticks.
Fan, Guihong +2 more
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Differential evolution for dynamic optimization of differential-algebraic systems
Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97), 2002An efficient method is introduced for solving optimal control and optimal parameter selection problems of nonlinear differential-algebraic systems involving general constraints. These infinite-dimensional problems are first converted into the uncaused optimal parameter selection problems.
null Feng-Sheng Wang, null Ji-Pyng Chiou
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Differential Forms and Dynamical Systems
2007One of the modern geometric views of dynamical systems is as vector fields on a manifold, with or without boundary. The starting point of this paper is the observation that, since one-forms are the natural expression of linear functionals on the space of vector fields, the interaction between the two makes some aspects of the study of equilibria and ...
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Dynamical Systems and Differential Equations
2015In this chapter, we review some basic topics in the theory of ordinary differential equations from the viewpoints of the global geometrical approach which is a base to develop the energy flow analysis for NDS. In the first two sections the review of basic theory for dynamical systems and differential equations is rapid.
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Differential Equations and System Dynamics
2014In Chapter 5, we saw how we can simulate a continuous process given by the update equations which define the rate of change of the process in terms of the current and previous values of the process. A real world system is a combination of interdependent processes which may be hidden or visible to the outside world.
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Differential Equations and Dynamical Systems
2012Henri Poincare presented his thesis to the Faculte des Sciences of the University of Paris to obtain the degree of doctor of mathematical sciences. The title: “Sur les proprietes des fonctions definies par les equations aux differences partielles.” It was accepted on August 1, 1879, by a committee consisting of J.-C. Bouquet (chairman), P.-O.
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2009
This book aims to present a new approach called Flow Curvature Method that applies Differential Geometry to Dynamical Systems. Hence, for a trajectory curve, an integral of any n-dimensional dynamical system as a curve in Euclidean n-space, the curvature of the trajectory — or the flow — may be analytically computed.
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This book aims to present a new approach called Flow Curvature Method that applies Differential Geometry to Dynamical Systems. Hence, for a trajectory curve, an integral of any n-dimensional dynamical system as a curve in Euclidean n-space, the curvature of the trajectory — or the flow — may be analytically computed.
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