Results 21 to 30 of about 50,631 (294)
Bifurcations of periodic orbits and uniform approximations. [PDF]
, 1997 We derive uniform approximations for contributions to Gutzwiller's periodic-orbit sum for the spectral density which are valid close to bifurcations of periodic orbits in systems with mixed phase space.
Schomerus, Henning, Sieber, Martin
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IEEE Transactions on Automatic Control, 2004 A parametrized nonlinear differential equation can have multiple equilibria as the parameter is varied. A local bifurcation of a parametrized differential equation occurs at an equilibrium where there is a change in the topological character of the nearby solution curves.
Krener, Arthur J. +2 more
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IEEE Access, 2022 In this work, we describe the model of a new 5-D hyperchaotic system with three positive Lyapunov exponents. Since the maximum positive Lyapunov exponent of the proposed hyperchaotic system is larger than twelve, the new hyperchaotic system is highly ...
Khaled Benkouider +9 more
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Gated Recurrent Units Viewed Through the Lens of Continuous Time Dynamical Systems
Frontiers in Computational Neuroscience, 2021 Gated recurrent units (GRUs) are specialized memory elements for building recurrent neural networks. Despite their incredible success on various tasks, including extracting dynamics underlying neural data, little is understood about the specific dynamics
Ian D. Jordan +5 more
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Tipping the Balance: A Criticality Perspective
Entropy, 2022 Cell populations are often characterised by phenotypic heterogeneity in the form of two distinct subpopulations. We consider a model of tumour cells consisting of two subpopulations: non-cancer promoting (NCP) and cancer-promoting (CP).
Indrani Bose
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Arab Journal of Basic and Applied Sciences, 2022 The classic Lotka–Volterra model is a two-dimensional system of differential equations used to model population dynamics among two-species: a predator and its prey. In this article, we consider a modified three-dimensional fractional-order Lotka–Volterra
Feras Yousef +2 more
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Singularity bifurcations [PDF]
Journal of Macroeconomics, 2006 equation models represent an important class of macroeconomic systems. Our ongoing research (He and Barnett (2003)) on the Leeper and Sims (1994) Euler equations macroeconometric model is revealing the existence of singularity-induced bifurcations, when the model¡¯s parameters are within a confidence region about the parameter estimates. Although known
Yijun He, William Barnett
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Bifurcations of piecewise smooth flows:perspectives, methodologies and open problems [PDF]
, 2012 In this paper the theory of bifurcations in piecewise smooth flows is critically surveyed. The focus is on results that hold in arbitrarily (but finitely) many dimensions, highlighting significant areas where a detailed understanding is presently lacking ...
A. Colombo +10 more
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The flatness of bifurcations in 3D dendritic trees: an optimal design
Frontiers in Computational Neuroscience, 2012 The geometry of natural branching systems generally reflects functional optimization. A common property is that their bifurcations are planar and that daughter segments don’t turn back in the direction of the parent segment.
Jaap evan Pelt, Harry B M Uylings
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IEEE Access, 2021 In this work, we describe the model of a new 4-D hyperchaotic system with no balance point and deduce that the new hyperchaotic system has a hidden attractor.
Sundarapandian Vaidyanathan +9 more
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