Frank Hoppensteadt
American mathematician
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Mathematics
Frank Hoppensteadt'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 Frank Hoppensteadt Influential?
(Suggest an Edit or Addition)According to Wikipedia, Frank Charles Hoppensteadt is an American mathematician, specializing in mathematical biology and dynamical systems. Frank Hoppensteadt studied physics and mathematics at Butler University with bachelor's degree in 1960. At the University of Wisconsin–Madison, he received in 1962 his master's degree and in 1965 his PhD with thesis Singular perturbations on the infinite interval under the supervision of Fred Guenther Brauer and Wolfgang Wasow. From 1965 Hoppensteadt was an assistant professor at Michigan State University in East Lansing. From 1968 he was an associate professor and later a professor at New York University's Courant Institute until his resignation in 1979. From 1977 to 1986 he was a professor at the University of Utah, where he also chaired the mathematics department. From 1986 he was Dean of Natural Science at Michigan State University and then, from 1995, at Arizona State University, Professor of Mathematics and Electrical Engineering and Director of the Center for Systems Science and Engineering Research. From 2004 he was Senior Vice Provost for Planning at New York University, and then from 2006 Research Professor at New York University's Courant Institute until his retirement in 2012.
Frank Hoppensteadt's Published Works
Published Works
- Weakly connected neural networks (1997) (1093)
- Heterogeneity in oscillator networks: are smaller worlds easier to synchronize? (2003) (736)
- Bursts as a unit of neural information: selective communication via resonance (2003) (550)
- Pattern recognition via synchronization in phase-locked loop neural networks (2000) (346)
- Singular perturbations on the infinite interval (1966) (302)
- CBMS-NSF REGIONAL CONFERENCE SERIES IN APPLIED MATHEMATICS (2010) (292)
- INTEGRATE-AND-FIRE MODELS OF NERVE MEMBRANE RESPONSE TO OSCILLATORY INPUT. (1981) (278)
- Properties of solutions of ordinary differential equations with small parameters (1971) (217)
- Analysis and simulation of chaotic systems (1992) (183)
- Oscillatory Neurocomputers with Dynamic Connectivity (1999) (161)
- Synchronization of MEMS resonators and mechanical neurocomputing (2001) (142)
- Modeling and Simulation in Medicine and the Life Sciences (2001) (141)
- An Age Dependent Epidemic Model (1974) (139)
- Thalamo-cortical interactions modeled by weakly connected oscillators: could the brain use FM radio principles? (1998) (139)
- Mathematical methods of population biology (1982) (129)
- Dynamics of the Josephson junction (1978) (124)
- Conditions for sympatric speciation: A diploid model incorporating habitat fidelity and non-habitat assortative mating (1996) (115)
- Random Perturbation Methods with Applications in Science and Engineering (2002) (114)
- Asymptotic stability in singular perturbation problems. II: Problems having matched asymptotic expansion solutions☆ (1974) (107)
- Frequency Entrainment of a Forced van der pol Oscillator. (1977) (101)
- Classification of bursting Mappings (2004) (97)
- An introduction to the mathematics of neurons (1986) (97)
- Synaptic organizations and dynamical properties of weakly connected neural oscillators (1996) (84)
- Synchronization of periodical cicada emergences. (1976) (82)
- Multitime Methods for Systems of Difference Equations (1977) (76)
- Asymptotic stability in singular perturbation problems (1968) (75)
- Spin-wave interference patterns created by spin-torque nano-oscillators for memory and computation (2010) (74)
- Phase locking of biological clocks (1982) (71)
- Synaptic organizations and dynamical properties of weakly connected neural oscillators II. Learning phase information (1996) (66)
- Capacity of oscillatory associative-memory networks with error-free retrieval. (2004) (65)
- A problem in the theory of epidemics (1970) (63)
- Polychronous Wavefront Computations (2009) (62)
- Mathematics in medicine and the life sciences (1992) (56)
- Phase clustering and transition to phase synchronization in a large number of coupled nonlinear oscillators. (2001) (53)
- Periodic Solutions of a Logistic Difference Equation (1977) (49)
- Photoperiodic induction of diurnal locomotor activity in Microtus montanus, ,the montane vole (1982) (46)
- An Introduction to the Mathematics of Neurons: Modeling in the Frequency Domain (1997) (45)
- Predator-prey model (2006) (43)
- A problem in the theory of epidemics, II (1971) (41)
- Stability in systems with parameter (1967) (35)
- Characterization of neural interaction during learning and adaptation from spike-train data. (2004) (33)
- On systems of ordinary differential equations with several parameters multiplying the derivatives (1969) (33)
- Oscillatory model of novelty detection (2001) (33)
- Smallest small-world network. (2002) (33)
- Pattern formation by bacteria (1980) (33)
- An Algorithm for Approximate Solutions to Weakly Filtered Synchronous Control Systems and Nonlinear Renewal Processes (1983) (31)
- A hysteresis model for bacterial growth patterns (1984) (30)
- An oscillatory neural network model of sparse distributed memory and novelty detection. (2000) (29)
- Oscillatory models of the hippocampus: A study of spatio-temporal patterns of neural activity (1999) (29)
- Mathematical aspects of physiology (1981) (28)
- The searchlight hypothesis (1991) (28)
- Slowly Modulated Oscillations in Nonlinear Diffusion Processes (1977) (28)
- Oscillatory associative memory network with perfect retrieval (2004) (27)
- Intermittent chaos, self-organization, and learning from synchronous synaptic activity in model neuron networks. (1989) (27)
- Implementation of Minimum Inventory Variability Scheduling 1-Step Ahead Policy(R) in a large semiconductor manufacturing facility (1997) (26)
- Probing Changes in Neural Interaction During Adaptation (2003) (26)
- Nonlinear Oscillations in Biology (1979) (26)
- Numerical solution of Volterra integral and integro-differential equations with rapidly vanishing convolution kernels (2007) (24)
- Theoretical analysis of divergence in mean fitness between initially identical populations (1995) (24)
- Memorizing and recalling spatial-temporal patterns in an oscillator model of the hippocampus. (1998) (24)
- Slowly Coupled Oscillators: Phase Dynamics and Synchronization (2003) (24)
- Canonical Neural Models (2001) (22)
- Spin wave excitation patterns generated by spin torque oscillators (2013) (20)
- On plasmid incompatibility. (1978) (19)
- Numerical and experimental investigation of the effect of filtering on chaotic symbolic dynamics. (2003) (17)
- INDIA'S APPROACH TO ELIMINATING PLASMODIUM FALCIPARUM MALARIA: A MODELING PERSPECTIVE (2010) (17)
- Differential equations having rapidly changing solutions: Analytic methods for weakly nonlinear systems (1976) (17)
- Threshold analysis of a drug use epidemic model (1981) (17)
- Analysis and computer simulation of accretion patterns in bacterial cultures (1994) (15)
- Analysis of a stable polymorphism arising in a selection-migration model in population genetics (1975) (15)
- On quasilinear parabolic equations with a small parameter (1971) (14)
- A slow selection analysis of two locus, two allele traits. (1976) (14)
- Unfolding an electronic integrate-and-fire circuit (2010) (14)
- Asymptotic Behavior of Solutions to a Population Equation (1975) (14)
- Oscillatory model of novelty detection. (2001) (12)
- Quasi-Static State Analysis of Differential, Difference, Integral, and Gradient Systems (2010) (10)
- Nonlinear stability analysis of static states which arise through bifurcation (1975) (10)
- Numerical Treatment of Rapid Chemical Kinetics by Perturbation and Projection Methods (1981) (10)
- Distortion of optical properties in cylinders by absorbance flattening (1972) (10)
- Mathematical Modelling in Epidemiology (J. C. Frauenthal) (1983) (9)
- Cooperation of spike timing-dependent and heterosynaptic plasticities in neural networks: a Fokker-Planck approach. (2006) (9)
- Investigation of minimum inventory variability scheduling policies in a large semiconductor manufacturing facility (1997) (8)
- Getting Started in Mathematical Biology (1997) (8)
- Asymptotic series solutions of some nonlinear parabolic equations with a small parameter (1969) (8)
- Mathematical Aspects of Population Biology (1978) (7)
- Iterated averaging methods for systems of ordinary differential equations with a small parameter (1978) (7)
- An averaging principle for dynamical systems in Hilbert space with Markov random perturbations (1996) (7)
- Signal Processing by Model Neural Networks (1992) (7)
- Mathematical Methods for Analysis of a Complex Disease (2011) (6)
- Heuristics for the Hodgkin-Huxley system. (2013) (6)
- Discrete time semigroup transformations with random perturbations (1997) (6)
- Analysis of Some Problems Having Matched Asymptotic Expansion Solutions (1975) (6)
- Numerical methods for stiff systems of differential equations related with transistors, tunnel diodes, etc (1973) (6)
- Modeling the Cumulative Distribution Function of Spikes in Neural Networks (2004) (6)
- Numerical solution of a problem in the theory of epidemics (2006) (6)
- Did Something Change? Thresholds in Population Models (2003) (6)
- Cauchy problems involving a small parameter (1970) (6)
- Asymptotic series solutions for nonlinear ordinary differential equations with a small parameter (1969) (6)
- Associative memory of weakly connected oscillators (1997) (6)
- An Extrapolation Method for the Numerical Solution of Singular Perturbation Problems (1983) (5)
- Randomly Perturbed Volterra Integral Equations And Some Applications (1995) (5)
- Thresholds for Deterministic Epidemics (1974) (5)
- Asymptotic solutions of linear partial differential equations of first order having random coefficients (1994) (5)
- Optimal exploitation of a spatially distributed fishery (1977) (5)
- Spin torque oscillator neuroanalog of von Neumann's microwave computer (2015) (4)
- Markov Chains with Random Transition Probabilities (2002) (4)
- A particle method for population shock waves with application to synchronization of bacterial culture growth (1995) (4)
- Weakly Connected Oscillators (1997) (4)
- Theoretical Immunology (George I. Bell, Alan S. Perelson and George H. Pimbley, Jr., eds.) (1979) (4)
- A theory of epineuronal memory (2004) (4)
- Control of Cell Volume and the Electrical Properties of Cell Membranes (1992) (4)
- Oscillations of Linear Systems (1993) (4)
- Bifurcations in brain dynamics (1996) (4)
- Interdisciplinary Research On Modeling And Scheduling Of Semiconductor Manufacturing Operations (2000) (4)
- A Theory of Epidemics (1992) (4)
- Canonical models for mathematical neuroscience (1997) (4)
- Computation by Extrapolation of Solutions of Singular Perturbation Problems (1981) (3)
- A Mini-FAB simulation model comparing FIFO and MIVP(R) schedule policies (outer loop), and PID and H/sup /spl infin// machine controllers (inner loop) for semiconductor diffusion bay maintenance (1998) (3)
- Activity patterns in networks stabilized by background oscillations (2009) (3)
- Voltage-controlled oscillations in neurons (2006) (3)
- Synchronization of Bacterial Culture Growth (1989) (3)
- Diffusion bay simulation and its impact on the overall FAB performance: a simplified example (2003) (3)
- On the asymptotic behavior of Markov chains with small random perturbations of transition probabilities (1996) (2)
- Local Analysis of Weakly Connected Maps (1997) (2)
- Applied physics: A new spin on nanoscale computing (2017) (2)
- Biologically Inspired Circuits: Coalition Formation in Aggregates (2006) (2)
- Markov chain with small random perturbations with applications to Bacterial Genetics (1996) (2)
- Anisotropic spin-wave patterns generated by spin-torque nano-oscillators (2011) (2)
- A geometric approach to boundary value problems for nonlinear ordinary differential equations with a small parameter (1971) (2)
- Thalamo-cortical interactions modeled by forced weakly connected oscillatory networks (1997) (2)
- A Multiple Species Fishery Model: An Input-Output Approach (1981) (2)
- Models in Population Biology (2002) (2)
- Mathematical methods of population biology: Preface (1982) (1)
- A Frequency-Phase Potential for a Forced STNO Network: an Example of Evoked Memory (2020) (1)
- Biological Clocks and Mechanisms of Neural Control (1992) (1)
- Synchronized oscillations in networks of neuron analogue circuits. (1984) (1)
- Computer simulation of a neural prism (1989) (1)
- PROPAGATING COALITIONS IN NETWORKS OF NONLINEAR OSCILLATORS (2006) (1)
- Singular Perturbation Solutions of Noisy Systems (1995) (1)
- Conditions for sympatric speciation: a diploid incorporating habitat fidelity and non-habitat assortative mating model (1996) (1)
- Methods of Averaging (1993) (1)
- An analysis of transient behavior in the onset of convection (1977) (1)
- Neural computations by networks of oscillators (2000) (1)
- Synaptic Organizations of the Brain (1997) (1)
- Stable oscillations of weakly nonlinear Volterra integro-differential equations. (1984) (1)
- Minimum Inventory Variability Dispatching Policies (Mivp) (2000) (1)
- Local Analysis of Singularly Perturbed WCNNs (1997) (1)
- Dynamical Systems on a Torus (2002) (1)
- Bifurcations in Neuron Dynamics (1997) (1)
- An averaging method for Volterra integral equations with applications to phase-locked feedback systems (1983) (1)
- Random Perturbation Methods with Applications in Science and Engineering. Applied Mathematical Sciences, Vol 150 (2003) (1)
- Gas Exchange in the Lungs (1992) (1)
- Nonlinear Phenomena in Electromagnetic Theory and Acoustics. (1978) (1)
- The heart and circulation (1979) (1)
- QSSA for boundary layer problems (2010) (0)
- Smallest Small-World Networks Smallest small-world network (2018) (0)
- Mathematical methods of population biology: References (1982) (0)
- Perturbation Methods in Applied Mathematics. By J. KEVORKIAN and J. D. COLE. Springer, 1981. 558 pp. DM 96. (1984) (0)
- Response of a solutivory chain to a nutrient pulse (1994) (0)
- Averaging over random noise (2010) (0)
- Quasistatic-State Methods (1993) (0)
- Mathematical biology (2007) (0)
- Proliferation, Spread and Reaction-Dispersal Processes (1980) (0)
- Applications of multi-time methods to pattern recognition and other problems (1977) (0)
- The Renal Countercurrent Mechanism (1992) (0)
- Algebraic and Topological Aspects of Nonlinear Oscillations (1993) (0)
- Stability of Nonlinear Systems (1993) (0)
- 10 Did something change ? Thresholds in Population Models (2009) (0)
- Local Analysis of WCNNs (1997) (0)
- Convergence Properties of Stochastic Processes (2002) (0)
- Regular Perturbation Methods (1993) (0)
- Phase-Locked Loops (2002) (0)
- The Mathematics of Populations: Demographics (1992) (0)
- Asymptotic stability and singular perturbations (2010) (0)
- Mathematical methods of population biology: Renewal theory and reproduction matrices (1982) (0)
- Slow selection analysis of genetic traits in synchronized populations (1979) (0)
- Book reviews (1997) (0)
- System of Phase Oscillators with Diagonalizable Interaction (2003) (0)
- Analysis of a VCON Neuromime (1986) (0)
- Solutions to selected exercises (1982) (0)
- Propagation of epidemic diseases (2011) (0)
- The Neural Basis of Motor Control, Vernon B. Brooks. Oxford University Press (1986), U.S.$45 (cloth), 330 pp (1989) (0)
- Book reviews (1989) (0)
- Averaging differential equations (2010) (0)
- Quasi-Static Bifurcations (1997) (0)
- Analysis of a VeON Neufomime (1986) (0)
- MULTI-SCALE METHODS, COMPUTER SIMULATIONS AND DATA MINING: DIFFERENCE EQUATIONS AND RENEWAL EQUATIONS (2008) (0)
- Stratifications of disease systems (2011) (0)
- Introduction to Part 1 (2010) (0)
- Multiple Andronov-Hopf Bifurcation (1997) (0)
- Other singular perturbation problems (2010) (0)
- Oscillatory model of the hippocampal memory (1999) (0)
- Frequency Modulation Dynamics in Neural Networks a (1987) (0)
- Introduction to Canonical Models (1997) (0)
- The dynamics of small neural populations: by John Milton, CRM monograph series, volume 7, American Mathematics Society, Providence, RI, 1996. $35.00 (cloth), xviii + 125 pp (1997) (0)
- Introduction to Part 2 (2010) (0)
- Saddle-Node on a Limit Cycle (1997) (0)
- Numerical solution of Volterra integro‐differential equations modelling thalamo‐cortical systems (2007) (0)
- Appendix: Circuit theory (2010) (0)
- Spin Wave Neuroanalog of von Neumann's Microwave Computer (2014) (0)
- RANDOM PERTURBATIONS OF VOLTERRA DYNAMICAL SYSTEMS IN NEUROSCIENCE (2003) (0)
- A mathematical analysis of small mammal populations (1987) (0)
- Randomly Perturbed Mechanical Systems (2002) (0)
- Spin torque nanooscillators: new applications in information processing (2013) (0)
- Patterns of Population Growth and Dispersal (2002) (0)
- A Particle Method for Population Waves (1994) (0)
- SOLUTIONS NEAR BIFURCATED STEADY STATES (1975) (0)
- Perturbation Methods in Biology (2010) (0)
- U.S.$45 (cloth), 330 ppVernon B. Brooks, The Neural Basis of Motor Control, Oxford University Press (1986). (1989) (0)
- Associative Memoryof Weakly Connected (1997) (0)
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