Marty Golubitsky
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American mathematician
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Chaos Theory
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Mathematics
Marty Golubitsky's Degrees
- PhD Mathematics University of California, Berkeley
- Masters Mathematics University of California, Berkeley
- Bachelors Mathematics University of California, Berkeley
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Why Is Marty Golubitsky Influential?
(Suggest an Edit or Addition)According to Wikipedia, Martin Aaron Golubitsky is an American Distinguished professor of mathematics at Ohio State University and the former director of the Mathematical Biosciences Institute. Biography Education Marty Golubitsky was born on April 5, 1945, in Philadelphia, Pennsylvania. He graduated with bachelor's degree in 1966 from the University of Pennsylvania and the same year got his master's there as well. He obtained his Ph.D. from Massachusetts Institute of Technology in 1970 where his advisor was Victor Guillemin.
Marty Golubitsky's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- Singularities and groups in bifurcation theory (1985) (3126)
- Stable mappings and their singularities (1973) (1873)
- Singularities and Groups in Bifurcation Theory: Volume I (1984) (489)
- Geometric visual hallucinations, Euclidean symmetry and the functional architecture of striate cortex. (2001) (402)
- Nonlinear dynamics of networks: the groupoid formalism (2006) (384)
- Symmetry in locomotor central pattern generators and animal gaits (1999) (361)
- The Symmetry Perspective: From Equilibrium to Chaos in Phase Space and Physical Space (2002) (336)
- Symmetry Groupoids and Patterns of Synchrony in Coupled Cell Networks (2003) (304)
- A Theory for Imperfect Bifurcation via Singularity Theory. (1979) (295)
- Patterns of Synchrony in Coupled Cell Networks with Multiple Arrows (2005) (268)
- The Symmetry Perspective (2002) (249)
- Hopf Bifurcation in the presence of symmetry (1984) (239)
- A modular network for legged locomotion (1998) (230)
- What Geometric Visual Hallucinations Tell Us about the Visual Cortex (2002) (214)
- Classification and Unfoldings of Degenerate Hopf Bifurcations (1981) (212)
- Fearful Symmetry: Is God a Geometer? (1992) (206)
- Symmetry-increasing bifurcation of chaotic attractors (1988) (158)
- Symmetries and pattern selection in Rayleigh-Bénard convection (1984) (156)
- Models of central pattern generators for quadruped locomotion I. Primary gaits (2001) (146)
- Imperfect bifurcation in the presence of symmetry (1979) (130)
- Pattern selection with O(3) symmetry (1984) (124)
- Central pattern generators for bipedal locomotion (2006) (119)
- Boundary conditions and mode jumping in the buckling of a rectangular plate (1979) (116)
- Primary instabilities and bicriticality in flow between counter-rotating cylinders (1988) (105)
- Some Curious Phenomena in Coupled Cell Networks (2004) (100)
- Symmetry and stability in Taylor Couette flow (1986) (100)
- Heteroclinic cycles involving periodic solutions in mode interactions with O(2) symmetry (1989) (99)
- Hopf bifurcation with dihedral group symmetry - Coupled nonlinear oscillators (1986) (90)
- Bifurcation on the hexagonal lattice and the planar Bénard problem (1983) (89)
- Symmetry in chaos (1992) (88)
- A QUALITATIVE STUDY OF THE STEADY-STATE SOLUTIONS FOR A CONTINUOUS FLOW STIRRED TANK CHEMICAL REACTOR* (1980) (86)
- Models of central pattern generators for quadruped locomotion. I. Primary gaits. (2001) (86)
- Generic bifurcation of Hamiltonian systems with symmetry (1987) (86)
- Coupled arrays of Josephson junctions and bifurcation of maps with SN symmetry (1991) (81)
- Pattern Formation in Continuous and Coupled Systems (1999) (79)
- The structure of symmetric attractors (1993) (79)
- Ponies on a merry-go-round in large arrays of Josephson junctions (1991) (78)
- Pattern formation and bistability in flow between counterrotating cylinders (1988) (77)
- Meandering of the Spiral Tip: An Alternative Approach (1997) (73)
- The Hopf Bifurcation (1985) (71)
- An unfolding theory approach to bursting in fast–slow systems (2001) (70)
- An Introduction to Catastrophe Theory and Its Applications (1978) (69)
- Convergence of the age structure: applications of the projective metric. (1975) (69)
- Planforms in two and three dimensions (1992) (68)
- Coupled cells with internal symmetry: I. Wreath products (1996) (68)
- Bifurcation analysis near a double eigenvalue of a model chemical reaction (1981) (64)
- The Recognition Problem (1985) (64)
- The geometry of resonance tongues: a singularity theory approach (2003) (60)
- Iterates of maps with symmetry (1988) (59)
- A classification of degenerate Hopf bifurcations with O(2) symmetry (1987) (58)
- Interior symmetry and local bifurcation in coupled cell networks (2004) (58)
- Multiparameter Bifurcation Theory (1986) (57)
- Time-reversibility and particle sedimentation (1991) (57)
- The Informational City: Economic Restructuring and Urban Development Reprint Edition (1989) (56)
- The constrained Liapunov-Schmidt procedure and periodic orbits (1995) (55)
- Scalar and pseudoscalar bifurcations motivated by pattern formation on the visual cortex (2001) (55)
- Homogeneous three-cell networks (2006) (52)
- Hopf Bifurcation from Rotating Waves and Patterns in Physical Space (2000) (51)
- Cycling chaos (1995) (50)
- Symmetry of attractors and the Karhunen-Loegve decomposition (1994) (50)
- Bifurcations with O(3) symmetry including applications to the Bénard problem (1982) (48)
- Bifurcations from regular quotient networks: A first insight (2009) (47)
- Heteroclinic cycles in rings of coupled cells (2000) (46)
- Patterns of Oscillation in Coupled Cell Systems (2002) (44)
- Primitive actions and maximal subgroups of Lie groups (1972) (43)
- Two-colour patterns of synchrony in lattice dynamical systems (2005) (42)
- Nilpotent Hopf Bifurcations in Coupled Cell Systems (2006) (39)
- Bifurcations from Synchrony in Homogeneous Networks: Linear Theory (2009) (38)
- Target Patterns and Spirals in Planar Reaction-Diffusion Systems (2000) (38)
- Bifurcation problems with hidden symmetries (1984) (37)
- Detecting the symmetry of attractors (1993) (36)
- Bifurcation and Symmetry (1992) (35)
- Recent advances in symmetric and network dynamics. (2015) (34)
- Order in Disorder. (Book Reviews: Symmetry in Chaos. A Search for Pattern in Mathematics, Art and Nature.) (1993) (33)
- The Bénard Problem, Symmetry and the Lattice of Isotropy Subgroups (1983) (31)
- The Morse Lemma in Infinite Dimensions via Singularity Theory (1983) (31)
- Homeostasis, singularities, and networks (2017) (31)
- Winding Numbers and Average Frequencies in Phase Oscillator Networks (2006) (30)
- Coupled Cells: Wreath Products and Direct Products (1994) (28)
- Symmetry and Pattern Formation in Coupled Cell Networks (1999) (28)
- Symmetric patterns in linear arrays of coupled cells. (1993) (28)
- Analysis of Homeostatic Mechanisms in Biochemical Networks (2017) (28)
- Hopf-Hopf mode interactions with O(2) symmetry (1986) (28)
- Contact equivalence for Lagrangian submanifolds (1975) (28)
- Rigid patterns of synchrony for equilibria and periodic cycles in network dynamics. (2016) (27)
- Mechanisms of Symmetry Creation (1992) (26)
- Network periodic solutions: patterns of phase-shift synchrony (2012) (26)
- Patterns of synchrony in lattice dynamical systems (2005) (25)
- A singularity theory analysis of a thermal‐chainbranching model for the explosion peninsula (1981) (25)
- Bifurcations on hemispheres (1991) (24)
- Spatiotemporal Symmetries in the Disynaptic Canal-Neck Projection (2007) (24)
- An example of moduli for singular symplectic forms (1976) (23)
- Bifurcation on the Visual Cortex with Weakly Anisotropic Lateral Coupling (2003) (23)
- Feed-forward networks, center manifolds, and forcing (2012) (22)
- Network periodic solutions: full oscillation and rigid synchrony (2010) (22)
- The Feed-Forward Chain as a Filter-Amplifier Motif (2009) (21)
- SYNCHRONY VERSUS SYMMETRY IN COUPLED CELLS (2005) (21)
- SYMMETRY, GENERIC BIFURCATIONS, AND MODE INTERACTION IN NONLINEAR RAILWAY DYNAMICS (1999) (21)
- SPIRALS IN SCALAR REACTION–DIFFUSION EQUATIONS (1995) (20)
- Primitive subalgebras of exceptional Lie algebras (1971) (20)
- Sensitive signal detection using a feed-forward oscillator network. (2007) (19)
- Synchrony-Breaking Bifurcation at a Simple Real Eigenvalue for Regular Networks 1: 1-Dimensional Cells (2011) (19)
- Bifurcations with local gauge symmetries in the Ginzburg-Landau equations (1992) (19)
- Periodically Forced Hopf Bifurcation (2011) (18)
- Derived Patterns in Binocular Rivalry Networks (2013) (18)
- Homeostasis with Multiple Inputs (2018) (17)
- Homeostasis in a feed forward loop gene regulatory motif. (2018) (17)
- Time-periodic spatially periodic planforms in Euclidean equivariant partial differential equations (1995) (17)
- An Example of Symmetry Breaking to Heteroclinic Cycles (1997) (17)
- The Abelian Hopf H mod K Theorem (2010) (16)
- Linear Algebra and Differential Equations Using MATLAB (1999) (16)
- Reduction and Dynamics of a Generalized Rivalry Network with Two Learned Patterns (2012) (16)
- Geometry of resonance tongues (2007) (16)
- Stability of shock waves for a single conservation law (1975) (15)
- The structure of infinitesimal homeostasis in input–output networks (2020) (15)
- Normal Forms and Unfoldings of Singular Strategy Functions (2015) (14)
- A Brief Introduction to the Central Ideas of the Theory (1985) (14)
- Network Symmetry and Binocular Rivalry Experiments (2014) (14)
- An algebraic criterion for symmetric Hopf bifurcation (1993) (14)
- Patterns in Square Arrays of Coupled Cells (1997) (13)
- Stability Computations for Nilpotent Hopf bifurcations in Coupled Cell Systems (2007) (13)
- Symmetry detectives for SBR attractors (1995) (12)
- Infinitesimal homeostasis in three-node input–output networks (2020) (12)
- Modulated rotating waves in O(2) mode interactions (1988) (12)
- Hopf Bifurcation with O(2) Symmetry (1988) (11)
- Coordinate changes for network dynamics (2017) (11)
- On the local stability of differential forms (1976) (11)
- Patterns on growing square domains via mode interactions (2008) (11)
- Rotating chemical waves in the Gray-Scott model (1992) (10)
- Applications of the Fourier Transform (2005) (9)
- AN ANALYSIS OF IMPERFECT BIFURCATION * (1979) (9)
- Symmetry in Chaos - A Search for Pattern in Mathematics, Art, and Nature (2. ed.) (2009) (8)
- Bifurcations on Fully Inhomogeneous Networks (2020) (8)
- Homogeneous coupled cell networks with s 3 -symmetric quotient (2007) (8)
- Pattern Formation in Continuous and Coupled Systems : A Survey Volume (1999) (8)
- Symmetry methods in mathematical biology (2015) (8)
- Input-Output Networks, Singularity Theory, and Homeostasis (2020) (7)
- Primitive subalgebras of exceptional Lie algebras. (1971) (7)
- SYMMETRY AND PATTERN FORMATION ON THE VISUAL CORTEX (2004) (7)
- Singularity theory of fitness functions under dimorphism equivalence (2016) (6)
- The nonexistence of globally stable forms (1976) (6)
- Dimorphism by Singularity Theory in a Model for River Ecology (2017) (6)
- Synchrony in Lattice Differential Equations (2006) (6)
- BURSTING IN COUPLED CELL SYSTEMS (2004) (6)
- Homeostasis despite instability. (2018) (5)
- Symmetries of periodic solutions for planar potential systems (1996) (5)
- A torus bifurcation theorem with symmetry (1990) (5)
- Bifurcations in Forced Response Curves (2015) (5)
- Symmetric Networks with Geometric Constraints as Models of Visual Illusions (2019) (5)
- Symmetry and pattern formation for a planar layer of nematic liquid crystal (2003) (4)
- Heteroclinic Cycles in Systems with D N Symmetry (1999) (4)
- The Symmetry of Generalized Rivalry Network Models Determines Patterns of Interocular Grouping in Four-Location Binocular Rivalry. (2019) (4)
- Periodic Solutions of Symmetric Hamiltonian Systems (2002) (4)
- Symmetric Chaos : How and Why Mike Field and (1995) (4)
- Bifurcation and symmetry : cross influence between mathematics and applications (1992) (3)
- Breaking indecision in multi-agent, multi-option dynamics (2022) (3)
- The Dynamics of Multi-agent Multi-option Decision Making (2019) (3)
- Bifurcation and Planar Pattern Formation for a Liquid Crystal (2003) (3)
- Symmetry types and phase-shift synchrony in networks (2016) (3)
- Coincidence of Homeostasis and Bifurcation in Feedforward Networks (2019) (2)
- Hopf Bifurcation with Symmetry (2002) (2)
- Symmetries on the edge of chaos (1993) (2)
- Rotation , Oscillation and Spike Numbers in Phase Oscillator Networks (2)
- Classification of infinitesimal homeostasis in four-node input–output networks (2022) (2)
- Introduction to Partial Differential Equations (2005) (2)
- Symmetry and Bifurcation in Biology (2)
- Spirals in Scalar Reaction-Di usion (1995) (1)
- Finite Difference Schemes for the Heat Equation (2005) (1)
- Animal Gaits and Symmetry (2012) (1)
- Mode Interactions with O(2) Symmetry (1988) (1)
- Steady-State Bifurcation (2002) (1)
- Heteroclinic Cycles in Rings of Coupled (2000) (1)
- Bifurcation with Z 2-Symmetry (1985) (1)
- Dynamics and Bifurcation in Networks: Theory and Applications of Coupled Differential Equations (2023) (1)
- Review: Tim Poston and Ian Stewart, Catastrophe theory and its applications (1979) (1)
- Equivariant Unfolding Theory (1988) (1)
- Symmetry and Neuroscience (1)
- Patterns in Physical and Biological Systems (2013) (1)
- Genericity, Bifurcation and Symmetry (1991) (1)
- XXHOMOGENEOUS COUPLED CELL NETWORKS WITHS 3-SYMMETRIC QUOTIENTManuela (2007) (1)
- Hidden Symmetry and Genericity (2002) (0)
- Orthogonality and General Fourier Series (2005) (0)
- 3. Patterns Everywhere (2009) (0)
- Classification of Subgroups of SO ( 2 ) ⊕ R (2010) (0)
- Infinitesimal homeostasis in three-node input–output networks (2020) (0)
- 1. Introduction to Symmetry and Chaos (2009) (0)
- Bifurcation From Group Orbits (2002) (0)
- Classification by Codimension (1985) (0)
- ON THE LOCAL STABILITY OF DIFFERENTIAL FORMS * 1 ) (2010) (0)
- An application of singularity theory to convection in a spherical shell (1980) (0)
- The Traction Problem for Mooney—Rivlin Material (1988) (0)
- A formula for a symmetry detective (1997) (0)
- Modeling Neural Activity: Celebrating Jack Cowan’s Career Symmetry of generalized rivalry network models determines patterns of interocular grouping in four-location binocular rivalry (2019) (0)
- Poisson's Equation in Two Space Dimensions (2005) (0)
- Normal Forms and Unfoldings of Singular Strategy Functions (2014) (0)
- A survey on the singularities and stability of differential forms (2019) (0)
- Various Equivalent Notions of Stability (1973) (0)
- Equivariant Normal Forms (1988) (0)
- Homeostasis in Three-Node Networks (2019) (0)
- Classification of Singularities. Part II: The Local Ring of a Singularity (1973) (0)
- Homeostasis and Network Invariants (2015) (0)
- Dynamics, Symmetry and PDEs. (1997) (0)
- Network Symmetry and Binocular Rivalry Experiments (2014) (0)
- The Liapunov—Schmidt Reduction (1985) (0)
- Symmetry-Breaking in Steady-State Bifurcation (1988) (0)
- An Example of Moduli (1985) (0)
- Singularity theory of fitness functions under dimorphism equivalence (2016) (0)
- Steady-State Bifurcations in Euclidean Equivariant Systems (2002) (0)
- Classification of Singularities. Part I: The Thom-Boardman Invariants (1973) (0)
- Symmetry and bifurcation in vestibular system (2007) (0)
- Symmetric Chaos Mike Field and (2016) (0)
- Workshop: Theory an Applications of Coupled Cell Networks (2006) (0)
- Reydon Symmetry and the Explanation of Organismal Form Commentary on (2013) (0)
- Derived Patterns in Binocular Rivalry Networks (2013) (0)
- Symmetry and Synchrony (2014) (0)
- 7. Symmetric Fractals (2009) (0)
- Dimorphism by Singularity Theory in a Model for River Ecology (2017) (0)
- 5. Symmetric Icons (2009) (0)
- The Heat Equation Revisited (2005) (0)
- The Wave Equation (2000) (0)
- Multiparameter bifurcation theory : proceedings of the AMS-IMS-SIAM Joint Summer Research Conference held July 14-20, 1985, with support from the National Science Foundation (1986) (0)
- Symmetry-Breaking in Hopf Bifurcation (1988) (0)
- Time Periodicity and Spatio-Temporal Symmetry (2002) (0)
- The Malgrange Preparation Theorem (1973) (0)
- 2. Planar Symmetries (2009) (0)
- Two‐Point Boundary Value Problems (2020) (0)
- A Singularity Theory Approach To Steady-State Bifurcation Theory (2017) (0)
- Partners in Crime: Math and Prime-Time TV (2006) (0)
- Two Degrees of Freedom Without Symmetry (1985) (0)
- A REMARK ON PERIODICALLY PERTURBED BIFURCATION (1981) (0)
- Group-Theoretic Preliminaries (1988) (0)
- Two Degrees of Freedom with ( Z 2 ⊕ Z 2 )-Symmetry (1985) (0)
- Homeostasis, singularities, and networks (2016) (0)
- 4. Chaos and Symmetry Creation (2009) (0)
- BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY (2004) (0)
- Analysis of Homeostatic Mechanisms in Biochemical Networks (2017) (0)
- Preliminaries on Manifolds (1973) (0)
- Patterns of Synchrony: From Animal Gaits to Binocular Rivalry (2016) (0)
- Further Examples of Hopf Bifurcation with Symmetry (1988) (0)
- Symmetry methods in mathematical biology (2015) (0)
- Pattern Formation in Large Domains 1 August to 23 December 2005 (2007) (0)
- Convergence of Fourier Series (2005) (0)
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