Dynamics and bifurcations Jack K. Hale
Publisher: Springer

This plot is known as a bifurcation diagram and is likely a familiar sight. The desire to locate regions in parameter space exhibiting interesting dynamics has led to the development of computational tools for the automatic discovery of bifurcation sets [10]. Homoclinic and heteroclinic phenomena. While chaotic dynamics are entirely deterministic, their sensitivity to initial conditions can trick the observer into seeing iid. PT-symmetric Double Well Potentials Revisited: Bifurcations, Stability and Dynamics. This set has been called a chaotic saddle (owing to its saddle-type instability) or .. In particular, the prospect of Whole Brain Emulation or architectures can produce identical dynamics. Like a bifurcation point in chaos theory, the old system either falls apart or emerges with a higher degree of order. For example, Helge Aufderheide, Lars Rudolf and Thilo Gross examined food web graphs and defined an equivalence relation over these graphs based on the bifurcation diagrams. €This marvellous book describes a wealth of biological features in terms of the structure of the underlying dynamical space, its bifurcations, and its attractors. Fritz Colonius, Lars Grune, Dynamics, Bifurcations and Control Publisher: Springer | ISBN: 3540428909 | edition 2002 | PDF | 303 pages | 16.5 mbThis book contains a selection of the papers p. Normally hyperbolic invariant manifolds (NHIM). Hyperbolicity: stable and unstable manifolds. Understanding the the dynamics of large networks of interacting systems such as computers or neurons is a fundamental technology for many transhumanist projects and undertakings. Despite the diversity of these examples, they are thought to share in common a universal dynamical mechanism, which is the existence in phase space of an unstable, fractal invariant set on which the dynamics are chaotic [2, 6]. 42 of Applied Mathematical Sciences (SpringerVerlag, 1983). Holmes, Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, vol. Author dwh Categories Past the second bifurcation, there are no longer states of the original continuum system. This paper analyzes the lateral dynamics of vehicles with a perturbation method for approximation of system equilibrium at the front wheel steering angle as part of a system linearization and local bifurcation analysis. It is verified that there exist some dynamical behaviors in this model, such as transcritical bifurcation, flip bifurcation, Hopf bifurcation, and chaos. Stochastic forcing – exhibit many interesting phenomena and different dynamical properties that are obtained in the unforced systems are modified, leading to the bifurcations and attractors with novel dynamical properties.