## Publications for Jeff Moehlis

Neuroscience Applications

Excitable Systems / Cardiac Arrhythmias

Circadian Oscillators

Oscillators

Collective Behavior

Energy Harvesting

Shear Flow Turbulence

Microelectromechanical Systems (MEMS)

Canards

Bifurcations with Exact and Weakly Broken Symmetry

Scholarpedia

Other Technical

Other

Articles About Music

### Neuroscience Applications

**Journal Articles**

Clustered desynchronization from high-frequency deep brain stimulation, (.pdf) with D. Wilson, PLOS Computational Biology, **11**, e1004673, 2015.
Better living through phase and isostable reduction, (.html) with D. Wilson, SIAM News, **48**(9), pp. 1, 3, 6, 2015.
Determining individual phase response curves from aggregate population data (.pdf) with D. Wilson, Physical Review E, **92**, Article 022902, 2015.
Optimal entrainment of heterogeneous noisy neurons (.pdf) with D. Wilson, A.B. Holt, and T.I. Netoff, Frontiers in Neuroscience, **7**, Article 192, 2015.
Selective averaging with application to phase reduction and neural control (.pdf) with G.S. Schmidt, D. Wilson, and F. Allgower, Nonlinear Theory and Its Applications, **5**, 424-435, 2014.
A Hamilton-Jacobi-Bellman approach for termination of seizure-like bursting (.pdf) with D. Wilson, Journal of Computational Neuroscience, **37**, 345-355, 2014. Accompanying computer code: HJB_Minimum_Time_Control.zip, HJB_Minimum_Energy_Control.zip.
Locally optimal extracellular stimulation for chaotic desynchronization of neural populations (.pdf) with D. Wilson, Journal of Computational Neuroscience, **37**, 243-257, 2014.
Optimal chaotic desynchronization for neural populations (.pdf) with D. Wilson, SIAM Journal on Applied Dynamical Systems, **13**,276-305, 2014. Associated movies: 90170_01.avi, 90170_02.avi
Global isochrons and phase sensitivity of bursting neurons (.pdf) with A. Mauroy, B. Rhoads, and I. Mezic, SIAM Journal on Applied Dynamical Systems, **13**, 306-338, 2014.
Minimum energy control for *in vitro* neurons (.pdf) with A. Nabi, T. Stigen, and T. Netoff, Journal of Neural Engineering, **10**, Article No. 036005, 2013.
Minimum energy desynchronizing control for coupled neurons (.pdf) with A. Nabi, M. Mirzadeh, and F. Gibou, Journal of Computational Neuroscience, **34**, 259-271, 2013.
Time optimal control of spiking neurons (.pdf), with A. Nabi, Journal of Mathematical Biology, **64**, 981-1004, 2012.
Single input optimal control for globally coupled neuron networks (.pdf), with A. Nabi, Journal of Neural Engineering, **8**, Article No. 065008, 2011.
Controlling spike timing and synchrony in oscillatory neurons (.pdf), with T. Stigen, T. Netoff, and P. Danzl , Journal of Neurophysiology, **105**, 2074-2082, 2011.
A continuation method for computing global isochrons (.pdf), with H. Osinga, SIAM Journal on Applied Dynamical Systems, **9**, 1201-1228, 2010. Associated animations: 77724_01.gif, 77724_02.gif, 77724_03.gif, 77724_04.gif, 77724_05.gif, 77724_06.gif
Charge-balanced spike timing control for phase models of spiking neurons, (.pdf), with P. Danzl and A. Nabi, Discrete and Continuous Dynamical Systems Series A, **28**, 1413-1435, 2010.
Controlling biological networks by time-delayed signals, (.pdf) with G. Orosz and R. M. Murray , Phil. Trans. Royal Soc. A, **368** 439-454, 2010.
Event-based minimum-time control of oscillatory neuron models: phase randomization, maximal spike rate increase, and desynchronization, with P. Danzl , J. Hespanha , (.pdf) Biological Cybernetics, **101**, 387-399, 2009.
Partial phase synchronization of neural populations due to random Poisson inputs, (.pdf) with P. Danzl , R. Hansen, G. Bonnet , Journal of Computational Neuroscience, **25**, 141-157, 2008.
The physics of optimal decision making: A formal analysis of performance in two-alternative forced choice tasks (.pdf) with R. Bogacz , E. Brown , P. Holmes , and J.D. Cohen , Psychological Review, **113**, 700-765, 2006.
Optimal inputs for phase models of spiking neurons (.pdf) , with E. Shea-Brown and H. Rabitz , ASME Journal of Computational and Nonlinear Dynamics **1**, 358-367, 2006.
Canards for a reduction of the Hodgkin-Huxley equations, (.pdf) Journal of Mathematical Biology **52**, 141-153, 2006.
Optimal decisions: from neural spikes, through stochastic differential equations, to behavior (.pdf) with P. Holmes , E. Shea-Brown , R. Bogacz , J. Gao, G. Aston-Jones , E. Clayton, J. Rajkowski,and J.D. Cohen , IEICE Trans. Fundamentals, **E88-A**, 2496-2503, 2005.
The influence of spike rate and stimulus duration on noradrenergic neurons, (.pdf) , with E. Brown , P. Holmes , E. Clayton, J. Rajkowski, and G. Aston-Jones , Journal of Computational Neuroscience, 2004, **17**, 13-29, 2004.
On the phase reduction and response dynamics of neural oscillator populations, (.pdf) with E. Brown and P. Holmes , Neural Computation **16**, 673-715, 2004.
**Book Chapters ** (* = refereed)

* Globally coupled oscillator networks, (.pdf) , (.ps) , with E. Brown , P. Holmes , in * Perspectives and Problems in Nonlinear Science: A Celebratory Volume in Honor of Larry Sirovich*, ed. E. Kaplan, J. Marsden, and K.R. Sreenivasan, Springer, pp. 183-215, 2003.
**Conference Proceedings ** (* = refereed)

* Selective averaging with application to phase reduction (.pdf), with G.S. Schmidt and F. Allgower, Proceedings of NOLTA 2013, pp. 491-494, 2013.
* Minimum energy spike randomization for neurons (.pdf), with A. Nabi, M. Mirzadeh, and F. Gibou, Proceedings of 2012 American Control Conference, pp. 4751-4756, 2012.
* Nonlinear hybrid control of phase models for coupled oscillators (.pdf), with A. Nabi, Proceedings of 2010 American Control Conference, pp. 922-923, 2010.
* Linear control of neuronal spike timing using phase response curves, (.pdf), with T. Stigen, T. Netoff, and P. Danzl , in Proceedings of the 31st Annual International Conference of the IEEE Engineering in Medicine and Biology Society, pp. 1541-1544, 2009.
Controlling neural clustering using delayed inputs, (.pdf) with G. Orosz , Proceedings of IFAC TDS 2009.
* Charge-balanced optimal inputs for phase models of spiking neurons,
(.pdf) with A. Nabi, Proceedings of ASME Dynamic Systems and Control Conference, DSCC2009-2541, 2009.
* Spike timing control of oscillatory neurons using impulsive and
quasi-impulsive charge-balanced inputs (.pdf), with P. Danzl . Proceedings of the 2008 American Control Conference, pp. 171-176, 2008.
* Event-based feedback control of nonlinear oscillators using phase response curves (.pdf), with P. Danzl . Proceedings of the IEEE 46th Conf. on Decision and Control, pp. 5806-5811, 2007.
* On the response of neurons to sinusoidal current stimuli: phase response curves and phase-locking, (.pdf) with M. J. Schaus, Proceedings of the IEEE 45th Conf. on Decision and Control, pp. 2376-2381, 2006.
How a biological decision network can implement a statistically optimal test, (.pdf) with R. Bogacz , E. Brown , P. Holmes and J.D. Cohen , Modelling Natural Action Selection: Proceedings
of an International Workshop, 3-8. AISB Press, Brighton, UK, 2005.
Optimal decisions: from neural spikes, through stochastic differential equations, to behavior, (.pdf) with P. Holmes , E. Brown , R. Bogacz , J. Gao , P. Hu, G. Aston-Jones , E. Clayton, J. Rajkowski, and J.D. Cohen , Proceedings of the International Symposium on Nonlinear Theory and its Applications (NOLTA2004), Fukuoka, Japan, 2004.
**Technical Reports **

Optimizing reward rate in two alternative choice tasks: Mathematical formalism, (.pdf) , with E. Brown , R. Bogacz , P. Holmes , and J.D. Cohen . Princeton Technical Report #04-01, Center for the Study of Brain, Mind, and Behavior, 2004.
**Book Review **

Review of "Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting" by E.M. Izhikevich, (.pdf) SIAM Review **50**, 397-401, 2008.

### Excitable Systems/Cardiac Applications

**Journal Articles **

Better living through phase and isostable reduction, (.html) with D. Wilson, SIAM News, **48**(9), pp. 1, 3, 6, 2015.
Extending phase reduction to excitable media: theory and applications (.pdf) with D. Wilson, SIAM Review, **57**201-222, 2015.
An energy-optimal methodology for synchronization of excitable media (.pdf) with D. Wilson, SIAM Journal on Applied Dynamical Systems, **13**, 944-957, 2014. Associated movie: 94285_01.avi.
Isostables, isochrons, and Koopman spectrum for the action-angle representation of stable fixed point dynamics (.pdf) with A. Mauroy and I. Mezic, Physica D **261**, 19-30, 2013. Corrigendum.

### Circadian Oscillators

**Journal Articles **

An energy-optimal approach for entrainment of uncertain circadian oscillators (.pdf) with D. Wilson, Biophysical Journal, **107**, 1744-1755, 2014.

### Oscillators

**Journal Articles **

Synchronization of identical oscillators coupled through a symmetric network with dynamics: a constructive approach with applications to the parallel operation of inverters, (.pdf), with L.A.B. Torres and J.P. Hespanha, IEEE Transactions on Automatic Control, **60** 3226-3241, 2015.
Desynchronization stochastically synchronized chemical oscillators, (.pdf), with R. Snari, M.R. Tinsley, D. Wilson, S. Faramarzi, T.I. Netoff, and K. Showalter, Chaos, **25**, 123116, 2015.
Improving the precision of noisy oscillators (.pdf), Physica D, **272**, 8-17, 2014.
Phase noise of oscillators with unsaturated amplifiers (.pdf) with E. Kenig, M.C. Cross, and K. Wiesenfeld, Physical Review E, **88**, 062922, 2013.
Weakly coupled parametrically forced oscillator networks: existence,
stability, and symmetry of solutions (.pdf), with P. Danzl , Nonlinear Dynamics, **59**, 661-680, 2010.
Designing the dynamics of globally coupled oscillators (.pdf), with G. Orosz and P. Ashwin, Progress in Theoretical Physics **122**,611-630, 2009.
for dynamics and control of neural oscillators, see Neuroscience Applications
**Conference Proceedings ** (* = refereed)

* Power supply synchronization without communications (.pdf), with Leonardo A.B. Torres and Joao Hespanha, in Proceedings of the 2012 IEEE Power Engineering Society General Meeting.
also see "Selective averaging with application to phase reduction" listed under Neuroscience Applications

### Collective Behavior

**Journal Articles **

Modeling individual topic-specific behavior and influence backbone networks in social media (.pdf) with P. Bogdanov, M. Busch, A.K. Singh, and B.K. Szymanski, Social Network Analysis and Mining, **4**, 204, 2014.
How the spatial position of individuals affects their influence on swarms: a numerical comparison of two popular swarm dynamics models (.pdf) with A. Kolpas, M. Busch, H. Li, I.D. Couzin, and L. Petzold, PLoS One, **8**, e58525, 2013.
On the homogeneous assumption and the logistic behavior of information propagation (.pdf) with M. Busch, Phys. Rev. E, **85**, 026102, 2012.
Group decision-making models for sequential tasks (.pdf) with M. Kimura, SIAM Review, **54**, 121-138, 2012.
On bifurcations in nonlinear consensus networks (.pdf) with V. Srivastava and F. Bullo, J. Nonlin. Sci., **21**, 875-895, 2011.
Analysis of a class of symmetric equilibrium configurations for a territorial model (.pdf) with M. Busch, Numer. Math. Theor. Meth. Appl., **3**, 143-161, 2010.
Robotic reactions: delay-induced patterns in autonomous vehicle systems (.pdf) with G. Orosz and F. Bullo, Phys. Rev. E, **81**, 025204, 2010.
Equilibrium configurations for a territorial model (.pdf), with R. Votel
D.A.W. Barton , T. Gotou, T. Hatanaka, and M. Fujita, SIAM Journal on Applied Dynamical Systems, **8**, 1234-1260, 2009. Associated movies: 71012_01.mpg , 71012_02.mpg , 71012_03.mpg , 71012_04.mpg , 71012_05.mpg , 71012_06.mpg , 71012_07.mpg
Optimal switching between coexisting stable collective motion states (.pdf),
with A. Kolpas, Applied Mathematics Letters **22** 600-604, 2009.
Coarse analysis of collective motion with different communication mechanisms (.pdf), with A. Kolpas, T.A. Frewen, and I.G. Kevrekidis , Mathematical Biosciences, **214**, 49-57, 2008.
Parallel simulation for a fish schooling model on a general-purpose graphics processing unit (.pdf), with H. Li , A.M. Kolpas , and L. Petzold , Concurrency and Computation: Practice and Experience, **21** 725-737, 2009.
Novel vehicular trajectories for collective motion from coupled oscillator steering control (.pdf), with M. Kimura, SIAM Journal on Applied Dynamical Systems, **7** 1191-1212, 2008.
Coarse-grained analysis of stochasticity-induced switching between collective motion states (.pdf), with A. Kolpas and I.G. Kevrekidis , Proceedings of the National Academy of Sciences USA, **104**, 5931-5935, 2007.
**Book Chapters** (* = refereed)

* Coarse collective dynamics of animal groups (.pdf), with T. A. Frewen, I. D. Couzin, A. Kolpas, R. Coifman, and I. G. Kevrekidis , in Coping with Complexity: Model Reduction and Data Analysis, ed. A. N. Gorban and D. Roose, Springer, Berlin, 299-309, 2011.
**Conference Proceedings ** (* = refereed)

* The social media genome: modeling individual topic-specific behavior in social media (.pdf), with P. Bogdanov, M. Busch, A.K. Singh, and B.K. Szymanski, Proceedings of 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, pp. 236-242, 2014.
* Delayed car-following dynamics for human and robotic drivers (.pdf), with G. Orosz and F. Bullo, Proceedings of the 2011 ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference.
* On bifurcations in nonlinear consensus networks (.pdf), with V. Srivastava and F. Bullo, Proceedings of 2010 American Control Conference, pp. 1647-1652, 2010.

### Energy Harvesting

**Journal Articles **

Dynamic analysis of a buckled asymmetric piezoelectric beam for energy harvesting (.pdf), with L. Van Blarigan, Chaos **26** 033107, 2016.
Low dimensional modeling of a non-uniform, buckled piezoelectric beam for vibrational energy harvesting (.pdf), with L. Van Blarigan and R. McMeeking, Smart Materials and Structures **24** 065012, 2015.
A broadband vibrational energy harvester (.pdf), with L. Van Blarigan and P. Danzl, Applied Physics Letters **100** 253904, 2012.
**Conference Proceedings** (* = refereed)

* Exploiting nonlinearity to provide adaptable energy harvesting, (.pdf) with B.E. DeMartini, J.L. Rogers, and K.L. Turner , Proceedings of ASME Dynamic Systems and Control Conference DSCC2009-2152, 2009.

### Shear Flow Turbulence

**Journal Articles **

Characterizing the edge of chaos for a shear flow model (.pdf), with L. Kim, Physical Review E **78** 036315, 2008.
Transient growth for streak-streamwise vortex interactions (.pdf), with L. Kim, Physics Letters A, **358**, 431-437, 2006.
Low-dimensional models for turbulent plane Couette flow in a minimal flow unit (.pdf) with T.R. Smith and P. Holmes , Journal of Fluid Mechanics, **538**, 71-110, 2005.
Low-dimensional modelling of turbulence using the proper orthogonal decomposition: A tutorial (.pdf) with T.R. Smith and P. Holmes , Nonlinear Dynamics, **41**, 275-307, 2005.
Periodic orbits and chaotic sets in a low-dimensional model for shear flows (.pdf) with H. Faisst and B. Eckhardt , SIAM Journal on Applied Dynamical Systems **4**, 352-376, 2005 Associated movies: 60614_01.mpg , 60614_02.mpg , 60614_03.mpg , 60614_04.mpg , 60614_05.mpg , 60614_06.mpg , 60614_07.mpg
Fractal lifetimes in the transition to turbulence (.pdf) with B. Eckhardt and H. Faisst, Chaos **14**, S11, 2004 (Gallery of Nonlinear Images).
A low-dimensional model for turbulent shear flows (.pdf) with H. Faisst and B. Eckhardt , New Journal of Physics, **6** Article No. 56, 2004. Associated movies: model_NBC_movie.mpg , model_MFU_movie.mpg
Models for turbulent plane Couette flow using the proper orthogonal decomposition, (.pdf) , (.ps) with T.R. Smith, P. Holmes , and H. Faisst, Phys. Fluids **14**, 2493-2507, 2002.
**Conference Proceedings ** (* = refereed)

* Modeling and control of minimal flow unit turbulence in plane Couette flow, (.pdf), (.ps), with T.R. Smith and P.J. Holmes . Proceedings of the IEEE 42nd Conf. on Decision and Control, pp. 2322-2327, 2003.
Minimal plane Couette flow turbulence: a low-dimensional, uncoupled model (.pdf) , with T.R. Smith and P. Holmes , in Nonlinear Dynamics in Fluids, ed. F. Marques and A. Meseguer, International Center for Numerical Methods in Engineering (CIMNE), Barcelona , pp. 111-114, 2003.
A model for turbulent plane Couette flow using the proper orthogonal decomposition (.pdf) , with T. Smith, P. Holmes , Conference Proceedings for the 12th International Couette-Taylor Workshop, 2001

### Microelectromechanical Systems (MEMS)

**Journal Articles **

Chaos for a microelectromechanical oscillator governed by the nonlinear
Mathieu equation (.pdf), with B.E. DeMartini, H.E. Butterfield, and K.L. Turner , Journal of Microelectromechanical Systems, **16**, 1314-1323, 2007.
Linear and nonlinear tuning of parametrically excited MEM oscillators (.pdf), with B. DeMartini J. Rhoads , K. Turner , and S. Shaw , Journal of Microelectromechanical Systems, **16**, 310-318, 2007.
Generalized parametric resonance in electrostatically-actuated microelectromechanical oscillators (.pdf) , with J.F. Rhoads , S.W. Shaw , K.L. Turner , B.E. DeMartini, and W. Zhang, Journal of Sound and Vibration, ** 296**, 797-829, 2006.
also see "Weakly coupled parametrically forced oscillator networks: existence, stability, and symmetry of solutions" listed under Coupled Oscillators
**Conference Proceedings ** (* = refereed)

* On the dynamics of coupled parametrically forced oscillators (.pdf), Proceedings of 2008 ASME Dynamic Systems and Control Conference, DSCC2008-2189, 2008.
Prediction and validation of chaotic behavior in an electrostatically actuated microelectromechanical oscillator, (.pdf) with B.E. DeMartini, H.E. Butterfield, and K.L. Turner , in Proceedings of Transducers '07.
Modeling of parameterically excited microelectromechanical oscillator dynamics with application to filtering, (.pdf) with B. DeMartini, K. Turner , S. Shaw , J. Rhoads , W. Zhang, Proceedings of IEEE Sensors 2005, 345-348, 2006.
* Nonlinear response of parametrically-excited MEMS, (.pdf) with J.F. Rhoads , S.W. Shaw , K.L. Turner , B.E. DeMartini, and W. Zhang, Proceedings of the ASME Design Engineering Technical Conferences, 20th Biennial Conference on Mechanical Vibration and Noise (Long Beach, California), Paper DETC2005-84603, 2005.

### Canards

**Journal Articles **

Feedback control of canards, (.pdf) with J. Durham, Chaos. **18**, 015110, 2008.
Canards in a surface oxidation reaction, (.pdf) , J. Nonlinear Sci. **12**, 319-345, 2002.
also see "Canards for a reduction of the Hodgkin-Huxley equations" listed under Neuroscience Applications

### Bifurcations with Exact and Weakly Broken Symmetry

**Journal Articles **

Heteroclinic dynamics in a model of Faraday waves in a square container (.pdf) with J. Porter and E. Knobloch , Physica D, **238**, 846-859, 2009.
Heteroclinic cycles and periodic orbits for the O(2)-equivariant 0:1:2 mode interaction (.pdf) with T.R. Smith and P. Holmes , Physica D, **211**, 347-376, 2005.
Effect of noise on excursions to and back from infinity (.pdf) Phys. Lett. A **284**, 172-183, 2001.
Wrinkled tori and bursts due to resonant temporal forcing (.pdf) with E. Knobloch , Physica D **151**, 99-124, 2001.
Bursts in oscillatory systems with broken D_4 symmetry (.pdf) with E. Knobloch , Physica D **135**, 263-304, 2000.
Chaotic direction-reversing waves (.pdf) with E. Knobloch and A. S. Landsberg , Phys. Lett. A **225**, 287-293, 1999.
Forced symmetry breaking as a mechanism for bursting (.pdf), (.ps) with E. Knobloch , Phys. Rev. Lett. **80**, 5329-5332, 1998.
**Book Chapters ** (* = refereed)

Burst mechanisms in hydrodynamics, (.pdf), (.ps), with E. Knobloch , in * Nonlinear Instability,Chaos and Turbulence, Volume II *, ed. L. Debnath and D. Riahi, Series: Advances in Fluid Mechanics, Computational Mechanics Publications, Southampton, pp. 237-287, 2000 (51 pages).
**Conference Proceedings ** (* = refereed)

Bursting mechanisms for hydrodynamical systems, (.pdf), (.ps), with E. Knobloch , in * Pattern Formation in Continuous and Coupled Systems: A Survey Volume *, ed. M. Golubitsky, D. Luss, and S. H. Strogatz, Series: IMA Volumes in Mathematics and its Applications, vol. 115, Springer-Verlag, New York, 157-174, 1999.
Bursts, (.pdf), (.ps), with E. Knobloch , in * IUTAM Symposium on New Applications of Nonlinear and Chaotic dynamics in Mechanics *, ed. F. C. Moon, Kluwer, Dordrecht, 51-60, 1999.
**Dissertation **

"Forced symmetry-breaking as a mechanism for bursting". Click here for the abstract, and here for the full thesis in gzipped postscript (.ps.gz) format (3.7MB, unzips to 22.5MB, 273 pages).

### Scholarpedia

Jeff Moehlis, Kresimir Josic , Eric T. Shea-Brown . (2006) Periodic orbit. Scholarpedia, 1(7):1358
Kresimir Josic , Eric T. Shea-Brown , Jeff Moehlis (2006) Isochron. Scholarpedia, 1(8):1361
Jeff Moehlis and Edgar Knobloch (2007) Equivariant dynamical systems. Scholarpedia, 2(10):2510
Jeff Moehlis and Edgar Knobloch (2007) Equivariant bifurcation theory. Scholarpedia, 2(9):2511

### Other Technical

**Journal Articles **

Point-to-point control near heteroclinic orbits: plant and controller optimality conditions (.pdf) with B.A. Paden, Automatica **49**, 352-3570, 2013.
Radiation of mixed layer near-inertial oscillations into the ocean interior (.pdf) with S. G. Llewellyn Smith , Journal of Physical Oceanography, **31** 1550-1560, 2001.
Eckhaus-Benjamin-Feir instability in systems with temporal modulation (.pdf) with E. Knobloch , Phys. Rev. E **54**, 5161-5168, 1996.
**Conference Proceedings ** (* = refereed)

A nonparametric adaptive nonlinear statistical filter, (.pdf), in Proceedings of the 53rd IEEE Conference on Decision and Control, with M. Busch, 2040-2057, 2014.
Effect of a simple storm on a simple ocean, (.pdf), (.ps), in *Stirring and Mixing, 1999 Summer Study Program in Geophysical Fluid Dynamics *, Woods Hole Oceanographic Institution. Also available from http://gfd.whoi.edu/proceedings.

### Other

IUTAM Symposium on 50 Years of Chaos in Kyoto, Dynamical Sytems Magazine, July 2012.
Dynamical Systems at the 2008 SIAM Annual Meeting, Dynamical Systems Magazine, October 2008.

### Articles About Music

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