Hiroe Oka

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All published works

Action	Title	Year	Authors
+ PDF Chat	Global Dynamics of Ordinary Differential Equations: Wall Labelings, Conley Complexes, and Ramp Systems	2024	Marcio Gameiro Tomáš Gedeon Hiroshi Kokubu Konstantin Mischaikow Hiroe Oka Bernardo Rivas Ewerton R. Vieira Daniel Gameiro
+	Equilibria and their Stability in Networks with Steep Sigmoidal Nonlinearities	2021	W.J. Duncan Tomáš Gedeon Hiroshi Kokubu Konstantin Mischaikow Hiroe Oka
+ PDF Chat	Equilibria and their Stability in Networks with Steep Sigmoidal Nonlinearities	2021	W.J. Duncan Tomáš Gedeon Hiroshi Kokubu Konstantin Mischaikow Hiroe Oka
+ PDF Chat	Global dynamics for steep nonlinearities in two dimensions	2016	Tomáš Gedeon Shaun Harker Hiroshi Kokubu Konstantin Mischaikow Hiroe Oka
+	Global Dynamics for Steep Sigmoidal Nonlinearities in Two Dimensions	2015	Tomáš Gedeon Shaun Harker Hiroshi Kokubu Konstantin Mischaikow Hiroe Oka
+ PDF Chat	A topological computation approach to the interior crisis bifurcation	2012	Hiroshi Kokubu Hiroe Oka
+ PDF Chat	Quantitative hyperbolicity estimates in one-dimensional dynamics	2008	Sarah Day Hiroshi Kokubu Stefano Luzzatto Konstantin Mischaikow Hiroe Oka Paweł Pilarczyk
+	The Conley index for fast–slow systems II: Multidimensional slow variable	2005	Tomáš Gedeon Hiroshi Kokubu Konstantin Mischaikow Hiroe Oka
+	None	2002	Tomáš Gedeon Hiroshi Kokubu Konstantin Mischaikow Hiroe Oka
+	Kneading sequences for symmetric PL bimodal maps (Problems on complex dynamical systems)	1998	S. Nakamura Hiroe Oka
+	Linear Grading Function and Further Reduction of Normal Forms	1996	Hiroshi Kokubu Hiroe Oka Duo Wang
+	Existence of infinitely many connecting orbits in a singularly perturbed ordinary differential equation	1996	Hiroshi Kokubu Konstantin Mischaikow Hiroe Oka
+	MULTIPLE HOMOCLINIC BIFURCATIONS FROM ORBIT-FLIP I: SUCCESSIVE HOMOCLINIC DOUBLINGS	1996	Hiroshi Kokubu Motomasa Komuro Hiroe Oka
+	Successive homoclinic doublings bifurcations from oribt-flip	1996	Motomasa Komuro Hiroshi Kokubu Hiroe Oka
+	Bifurcations toN-homoclinic orbits andN-periodic orbits in vector fields	1993	Masashi Kisaka Hiroshi Kokubu Hiroe Oka
+	Normal forms for constrained nonlinear differential equations. II. Bifurcation	1989	Leon O. Chua Hiroe Oka
+	Normal forms for constrained nonlinear differential equations. I. Theory	1988	Leon O. Chua Hiroe Oka
+	Constrained systems, characteristic surfaces, and normal forms	1987	Hiroe Oka
+	Constrained Lorenz-like attractors	1985	Hiroe Oka Hiroshi Kokubu

Common Coauthors

Coauthor	Papers Together
Hiroshi Kokubu	15
Konstantin Mischaikow	9
Tomáš Gedeon	7
Shaun Harker	2
Leon O. Chua	2
W.J. Duncan	2
Motomasa Komuro	2
Paweł Pilarczyk	1
Bernardo Rivas	1
Ewerton R. Vieira	1
Daniel Gameiro	1
Sarah Day	1
S. Nakamura	1
Stefano Luzzatto	1
Marcio Gameiro	1
Masashi Kisaka	1
Duo Wang	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Geometric singular perturbation theory for ordinary differential equations	1979	Neil Fenichel	4
+	Isolated Invariant Sets and the Morse Index	1978	Charles C. Conley	4
+	Normal forms for singularities of vector fields	1984	Shigehiro Ushiki	4
+ PDF Chat	Deterministic Nonperiodic Flow	1963	Edward N. Lorenz	3
+ PDF Chat	Singularities of vector fields	1974	Floris Takens	3
+ PDF Chat	Connected simple systems, transition matrices, and heteroclinic bifurcations	1992	Christopher McCord Konstantin Mischaikow	3
+ PDF Chat	The connection matrix theory for Morse decompositions	1989	Robert Franzosa	2
+	Periodic Solutions of Piecewise Affine Gene Network Models with Non Uniform Decay Rates: The Case of a Negative Feedback Loop	2009	Etienne Farcot Jean‐Luc Gouzé	2
+	Normal forms for nonlinear vector fields. I. Theory and algorithm	1988	Leon O. Chua Hiroshi Kokubu	2
+	Branching of double pulse solutions from single pulse solutions in nerve axon equations	1987	Eiji Yanagida	2
+	Passivity gains and the “secant condition” for stability	2005	Eduardo D. Sontag	2
+	Geometrical Methods in the Theory of Ordinary Differential Equations	1988	V. I. Arnold	2
+	The Sil'nikov problem, exponential expansion, strong λ-lemma, C1-linearization, and homoclinic bifurcation	1989	Bo Deng	2
+	Constrained systems, characteristic surfaces, and normal forms	1987	Hiroe Oka	2
+	Conley--Morse Databases for the Angular Dynamics of Newton's Method on the Plane	2016	Justin Bush Wes Cowan Shaun Harker Konstantin Mischaikow	2
+	Singular perturbations in foliations	1989	Gik Ikegami	2
+ PDF Chat	Connecting orbits in one-parameter families of flows	1988	James F. Reineck	2
+ PDF Chat	Asymptotic amplitudes and Cauchy gains: a small-gain principle and an application to inhibitory biological feedback	2002	Eduardo D. Sontag	2
+	The cusp horseshoe and its bifurcations in the unfolding of an inclination-flip homoclinic orbit	1994	Ale Jan Homburg Hiroshi Kokubu Martin Krupa	2
+	Lattice structures for attractors I	2014	William D. Kalies Konstantin Mischaikow Robert Vandervorst	2
+	Implicit differential equations: Some open problems	1976	Floris Takens	2
+	Differential Equations with Small Parameters and Relaxation Oscillations	1980	E. F. Mishchenko Николай Христович Розов	2
+ PDF Chat	Lorenz attractors through Šil'nikov-type bifurcation. Part I	1990	Marek Rychlik	2
+ PDF Chat	An Algorithmic Approach to Chain Recurrence	2005	William D. Kalies Konstantin Mischaikow Robert Vandervorst	2
+ PDF Chat	Connected simple systems and the Conley index of isolated invariant sets	1985	Dietmar Salamon	2
+	Homoclinic bifurcation at resonant eigenvalues	1990	S.N. Chow Bo Deng Bernold Fiedler	2
+	Constrained equations; a study of implicit differential equations and their discontinuous solutions	1976	Floris Takens	2
+	Eigenvalue regions for positive systems	2003	Luca Benvenuti Lorenzo Farina	2
+ PDF Chat	Transcriptional regulation by the numbers: applications	2005	Lacramioara Bintu Nicolas E. Buchler Hernán G. García Ulrich Gerland Terence Hwa Jané Kondev Thomas E. Kuhlman Rob Phillips	2
+ PDF Chat	Geometrical Methods in the Theory of Ordinary Differential Equations	1983	Vladimir I. Arnold	2
+	Normal forms for nonlinear vector fields. II. Applications	1989	Leon O. Chua Hiroshi Kokubu	1
+	Sustained Resonance for a Nonlinear System with Slowly Varying Coefficients	1983	Clark Robinson	1
+ PDF Chat	On Hyperbolic Plateaus of the Henon Map	2007	Zin Arai	1
+	Zeta Functions, Periodic Trajectories, and the Conley Index	1995	Christopher McCord Konstantin Mischaikow Marian Mrożek	1
+	THE FOUNDATIONS OF DIFFERENTIAL GEOMETRY	1962	Oswald Veblen	1
+	Homoclinic and heteroclinic bifurcations of Vector fields	1988	Hiroshi Kokubu	1
+	Constrained Lorenz-like attractors	1985	Hiroe Oka Hiroshi Kokubu	1
+	Critical manifolds, travelling waves, and an example from population genetics	1982	C. Conley Paul C. Fife	1
+	A characterization of the minimum cycle mean in a digraph	1978	Richard M. Karp	1
+	On the Detection and Dynamical Consequences of Orbits Homoclinic to Hyperbolic Periodic Orbits and Normally Hyperbolic Invariant Tori in a Class of Ordinary Differential Equations	1988	Stephen Wiggins	1
+	Solutions of singular constrained differential equations: A generalization of circuits containing capacitor-only loops and inductor-only cutsets	1984	Börje Häggman Peter Bryant	1
+	On Loops in the Hyperbolic Locus of the Complex Hénon Map and Their Monodromies	2007	Zin Arai	1
+	The dynamics of perturbations of the contracting Lorenz attractor	1993	A. Rovella	1
+ PDF Chat	Absolutely continuous invariant measures for one-parameter families of one-dimensional maps	1981	Michael Jakobson	1
+	Unique normal forms: The nilpotent Hamiltonian case	1991	Alberto Baider Jan A. Sanders	1
+ PDF Chat	Structural stability of Lorenz attractors	1979	John Guckenheimer R. F. Williams	1
+	The Dynamics of the Henon Map	1991	Michael Benedicks Lennart Carleson	1
+	Homoclinic twisting bifurcations and cusp horseshoe maps	1993	Bo Deng	1
+ PDF Chat	A refinement of the Conley index and an application to the stability of hyperbolic invariant sets	1987	Andreas Floer	1
+	Singularities and Groups in Bifurcation Theory	1988	Martin Golubitsky Ian Stewart David G. Schaeffer	1