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Titlebook: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields; John Guckenheimer,Philip Holmes Book 1983 Springer Science+B

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John Guckenheimer,Philip Holmescortical systems—the neocortical and the limbic. Fibers that connect two neurons within the telencephalon are called .. Fibers that connect a telencephalic neuron with a sub-telencephalic neuron (at the diencephalon, brainstem, or spinal cord) are called .. The association fibers can be divided into
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Introduction: Differential Equations and Dynamical Systems, approach which we develop in this book. After recalling the basic existence and uniqueness theorems, we consider the linear, homogeneous, constant coefficient system and then introduce nonlinear and time-dependent systems and concepts such as the Poincaré map and structural stability. We then revie
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An Introduction to Chaos: Four Examples, periodically forced single degree of freedom oscillators, a three-dimensional autonomous differential equation, and a two-dimensional map. The oscillators of van der Pol [1927] and Duffing [1918] originally arose as models in electric circuit theory and solid mechanics, respectively, while the Lore
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Local Bifurcations,ich appear in the defining systems of equations. As these parameters are varied, changes may occur in the qualitative structure of the solutions for certain parameter values. These changes are called . and the parameter values are called .. To the extent possible, we develop in this chapter and Chap
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Averaging and Perturbation from a Geometric Viewpoint,thods might be familiar to the reader who has studied nonlinear mechanics and perturbation theory, the present geometrical approach and the stress on obtaining approximations to Poincaré maps will probably be less familiar.
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