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1992
Publisher Summary This chapter presents an overview of the bifurcation theory. This theory is applicable to nonlinear differential equations. Given a nonlinear differential equation that depends on a set of parameters, the number of distinct solutions may change as the parameters change.
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Publisher Summary This chapter presents an overview of the bifurcation theory. This theory is applicable to nonlinear differential equations. Given a nonlinear differential equation that depends on a set of parameters, the number of distinct solutions may change as the parameters change.
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A Statistical Theory for Imperfect Bifurcation
SIAM Journal on Applied Mathematics, 1982An “honest” statistical method is presented to analyze the effects of imperfections and other disturbances on the bifurcation of solutions of nonlinear problems. First, uniformly valid asymptotic approximations of the solutions are obtained for any realization of the imperfections.
John G. Watson, Edward L. Reiss
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SIAM Review, 1989
The careful observation of the dynamics of a kite in flight hints at the possibility of multiple equilibrium states. An application of bifurcation theory to a simplified model of kite flight bears out this assertion by proving the existence of a limit point bifurcation in the wind velocity/kite string angle ...
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The careful observation of the dynamics of a kite in flight hints at the possibility of multiple equilibrium states. An application of bifurcation theory to a simplified model of kite flight bears out this assertion by proving the existence of a limit point bifurcation in the wind velocity/kite string angle ...
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Introduction to Bifurcation Theory
2014One-dimensional bifurcations are discussed for scalar equations and planar systems. Results on Hopf bifurcations for planar systems are derived using the Lyapunov function method and the Friedrich method.
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Bifurcation Theory and Bistability
2013In this chapter, we will recapitulate the essential concepts, definitions and theorems of the Lyapunov and Andronov stability theories of dynamical systems. The global aim is to prepare the reader for the mathematical abstraction of biological switches and hysteresis phenomena.
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An Overview of Bifurcation Theory
2002In this appendix we want to provide a brief introduction and discussion of the concepts of dynamical systems and bifurcation theory which has been used in the preceding sections. We refer the reader interested in a more thorough discussion of the mathematical results of dynamical systems and bifurcation theory to the books of Wiggins (1990) and ...
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