- F. M. Atay and S. Liu. Cheeger constants, structural balance, and spectral clustering analysis for signed graphs. Preprint.
- W. Lu and F. M. Atay. Stability of phase difference trajectories of networks of Kuramoto oscillators with time-varying couplings and intrinsic frequencies. SIAM J. Appl. Dynamical Systems, 17(1):457–483, 2018.
- F. M. Atay and L. Roncoroni. Lumpability of linear evolution equations in Banach spaces. Evolution Equations and Control Theory 6(1):15–34, 2017.
- F. M. Atay. On the duality between consensus problems and Markov processes, with application to delay systems. Markov Processes and Related Fields 22(3):537–553, 2016.
- F. M. Atay and B. Hua. On the symmetry of the Laplacian spectra of signed graphs. Linear Algebra and its Applications 495:24–37, 2016.
- W. Lu and F. M. Atay. Local pinning of networks of multi-agent systems with transmission and pinning delays. IEEE Trans. Automatic Control 61(9):2657–2662, 2016.
- Ö. Karabacak, B. Alikoç, F. M. Atay. Stability regions for synchronized τ-periodic orbits of coupled maps with coupling delay τ. Chaos 26(9):093101, 2016.
- L. Horstmeyer and F. M. Atay. Characterization of exact lumpability for vector fields on smooth manifolds. Differential Geometry and its Applications 48:46–60, 2016.
- F. M. Atay, S. Banisch, Ph. Blanchard, B. Cessac, E. Olbrich, D. Volchenkov. Perspectives on multi-level dynamics. Discontinuity, Nonlinearity, and Complexity 5(3):313–339, 2016.
- F. M. Atay. Controlling oscillations in nonlinear systems with delayed output feedback. In Control of Self-Organizing Nonlinear Systems (E. Schöll, S. Klapp, P. Hövel, eds.) 65–79, Springer, Berlin, 2016.
- F. M. Atay and D. Irofti. A delayed consensus algorithm in networks of anticipatory agents. In Proc. ECC 2016: European Control Conference, 1880–1885, 2016.
- D. Irofti and F. M. Atay. On the delay margin for consensus in directed networks of anticipatory agents. IFAC-PapersOnLine 49(10):206–-211, 2016. (13th IFAC Workshop on Time Delay Systems, TDS 2016.)
- F. M. Atay and H. Ruan. Symmetry analysis of coupled scalar systems under time delay. Nonlinearity 22:795–824, 2015.
- N. Punetha, R. Ramaswamy, and F. M. Atay. Bipartite networks of oscillators with distributed delays: Synchronization branches and multistability. Physical Review E 91:042906, 2015.
- N. Punetha, S. Ujjwal, F. M. Atay, and R. Ramaswamy. Delay-induced remote synchronization in bipartite networks of phase oscillators. Physical Review E 91:022922, 2015.
- R. Sipahi, F. M. Atay, and S.-I. Niculescu. Stability analysis of a constant time-headway driving strategy with driver memory effects modeled with distributed delays. IFAC-PapersOnLine 48(12):376–381, 2015.
- F. M. Atay and H. Tuncel. On the spectrum of the normalized Laplacian for signed graphs: Interlacing, contraction, and replication. Linear Algebra and its Applications 442:165–177, 2014.
- S. Louca and F. M. Atay. Spatially structured networks of pulse-coupled phase oscillators on metric spaces. Discrete and Continuous Dynamical Systems A 34(9):3703–3745, 2014.
- W. Lu, F. M. Atay, and J. Jost. Consensus in networks of discrete-time multi-agent systems: Dynamical topologies and delays. In Delay Systems: From Theory to Numerics and Applications (T. Vyhlidal et al., eds.), 155–168, Springer, Berlin, 2014.
- F. M. Atay. Some novel dynamics in delay-coupled networks of dynamical systems. In AIP Conf. Proceedings 1582:148–157, 2014.
- F. M. Atay. Network consensus under distributed transmission delays. In Proc. ECC 2014: European Control Conference, 1110–1114, 2014.
- F. M. Atay. The consensus problem in networks with transmission delays. Phil. Trans. Royal Society A 371:20120460, 2013.
- S. Louca and F. M. Atay. Stationary states in infinite networks of spiking oscillators with noise. SIAM J. Applied Dynamical Systems 12(1):415–449, 2013.
- S. Jalan, F. M. Atay, and J. Jost. Inferring global synchrony from local symbolic dynamics. In Applications of Chaos and Nonlinear Dynamics in Science and Engineering (S. Banerjee and L. Rondoni, eds.) Vol. 3, 161–170, Springer, Berlin, 2013.
- W. Qiao, F. M. Atay, and R. Sipahi. Graph Laplacian design for fast consensus of a LTI System with heterogeneous agent couplings and homogeneous inter-agent delays. In Proc. ASME 2013 Dynamic Systems and Control Conference, Paper No. DSCC2013-4020, pp. V002T21A006 (8 pages), 2013.
- F. Lagzi, F. M. Atay, and S. Rotter. Nonlinear dynamics of large-scale activity in “networks of networks”. BMC Neuroscience 14(Suppl 1):P331, 2013.
- J. T. Lizier, F. M. Atay, and J. Jost. Information storage, loop motifs, and clustered structure in complex networks. Physical Review E 86:026110, 2012.
- F. M. Atay. On delay-induced stability in diffusively coupled dynamical systems. Afrika Matematika 23:109–119, 2012. (Invited article for Springer inaugural issue.)
- F. M. Atay. Consensus in networks under transmission delays and the normalized Laplacian. In Time Delay Systems – Methods, Applications and New Trends (R. Sipahi et al., eds.), Lect. Notes in Control and Information Sciences 423:407–416, 2012.
- F. M. Atay. Patterns of synchrony in networks of coupled oscillators. Oberwolfach Reports vol.9, pp. 3581–82, 2012.
- M. Kirkilionis and F. M. Atay. Introduction to Special Issue ECCS’10 in Theory in Biosciences. Theory in Biosciences 131:59–60, 2012.
- A. Spiegler, T. R. Knoesche, K. Schwab, J. Haueisen, F. M. Atay. Modeling brain resonance phenomena using a neural mass model. PLoS Computational Biology 7(12):e1002298, 2011.
- F. M. Atay. Synchronization and emergence in complex systems. Pramana 77(5):855–863, 2011.
- G. C. Sethia, A. Sen, and F. M. Atay. Phase locked solutions and their stability in the presence of propagation delays. Pramana 77(5):905–915, 2011.
- W. Lu, F. M. Atay, and J. Jost. Consensus and synchronization in discrete-time networks of multi-agents with stochastically switching topologies and time delays. Networks and Heterogeneous Media 6:329–349, 2011.
- C. Masoller and F. M. Atay. Complex transitions to synchronization in delay-coupled networks of logistic maps. European Physical Journal D 62:119–126, 2011.
- F. M. Atay and J. Jost. Qualitative inference in dynamical systems. In Handbook of Statistical Systems Biology (M. P. H. Stumpf, D. J. Balding, and M. Girolami, eds.), 339–358, John Wiley & Sons Ltd., Chichester, UK, 2011.
- W. Lu, F. M. Atay, and J. Jost. Consensus and synchronization in delayed networks of mobile multi-agents. In Proc. 18th IFAC World Congress, 2362–2367, 2011.
- A. Spiegler, T. R. Knoesche, J. Haueisen, and F. M. Atay. Complex behavior in a modified Jansen and Rit neural mass model. BMC Neuroscience 12(Suppl 1):P5, 2011.
- F. M. Atay (ed.). Complex Time-Delay Systems. Springer-Verlag Berlin, 2010.
- F. M. Atay, S. Jalan, and J. Jost. Symbolic dynamics and synchronization of coupled map networks with multiple delays. Physics Letters A 375:130–135, 2010.
- M. Deger, M. Helias, S. Cardanobile, F. M. Atay, and S. Rotter. Nonequilibrium dynamics of stochastic point processes with refractoriness. Physical Review E 82:021129, 2010.
- A. Spiegler, S. J. Kiebel, F. M. Atay, and T. R. Knoesche. Bifurcation analysis of neural mass models: Impact of extrinsic inputs and dendritic time constants. NeuroImage 52:1041–1058, 2010.
- G. C. Sethia, A. Sen, and F. M. Atay. Synchronous solutions and their stability in nonlocally coupled phase oscillators with propagation delays. Physical Review E 81:056213, 2010.
- F. Bauer, F. M. Atay, and J. Jost. Synchronized chaos in networks of simple units. EPL (Europhysics Letters) 89:20002, 2010.
- F. M. Atay. Delay-induced stability: From oscillators to networks. In Complex Time-Delay Systems (F. M. Atay, ed.), 45–62, Springer-Verlag Berlin 2010.
- F. M. Atay. Consensus in networks under transmission delays and the normalized Laplacian. In Proc. 9th IFAC Workshop on Time Delay Systems, 277–282, 2010.
- F. M. Atay. Consensus in networks under transmission delays and the normalized Laplacian. Ulmer Seminare — Funktionalanalysis und Evolutionsgleichungen 15:11–20, 2010.
- A. Spiegler, T. R. Knoesche, and F. M. Atay. Periodically forced neural mass model: entrainment and complex behavior. BMC Neuroscience 11(Suppl 1):P7, 2010.
- F. Bauer, F. M. Atay, and J. Jost. Synchronization in discrete-time networks with general pairwise coupling. Nonlinearity 22:2333–2351, 2009.
- F. M. Atay, S. Jalan, and J. Jost. Randomness, chaos, and structure. Complexity 15:29–35, 2009.
- F. M. Atay. Synchronization and amplitude death in coupled limit cycle oscillators with time delays. In Topics in Time Delay Systems (J. J. Loiseau et al., eds.), Lect. Notes in Control and Information Sciences 388:383–389, 2009.
- F. M. Atay. Stability of diffusively coupled difference equations with delays. In Proc. ICDEA 2008: 14th Int. Conf. on Difference Equations and Applications (M. Bohner et al., ed.), 133–139, 2009.
- F. M. Atay. Delayed feedback control near Hopf bifurcation. Discrete and Continuous Dynamical Systems – S 1:197–205, 2008.
- W. Lu, F. M. Atay, and J. Jost. Chaos synchronization in networks of coupled maps with time-varying topologies. European Physical Journal B 63:399–406, 2008.
- G. C. Sethia, A. Sen, and F. M. Atay. Clustered chimera states in delay-coupled oscillator systems. Physical Review Letters 100:144102, 2008.
- R. Sipahi, F. M. Atay, and S.-I. Niculescu. Stability of traffic flow behavior with distributed delays modeling the memory effects of the drivers. SIAM J. Applied Math. 68(3):738–759, 2007.
- W. Lu, F. M. Atay, and J. Jost. Synchronization of discrete-time dynamical networks with time-varying couplings. SIAM J. Math. Analysis 39(4):1231–1259, 2007.
- A. Hutt and F. M. Atay. Spontaneous and evoked activity in extended neural populations with gamma-distributed spatial interactions and transmission delay. Chaos, Solitons & Fractals 32:547–560, 2007.
- F. M. Atay. Networks with delays. In Network: From Biology to Theory, (J. Feng, J. Jost and M. Qian, eds.), 23–33, Springer-Verlag, 2007.
- F. M. Atay and A. Hutt. Dynamics of neural fields with distributed transmission speeds. In Mathematical Modeling of Biological Systems, Vol. II (A. Deutsch et al., ed.), 213–221, Birkhäuser Boston, 2007.
- R. Sipahi, S.-I. Niculescu, and F. M. Atay. Effects of short-term memory of drivers on stability interpretations of traffic flow dynamic dynamics. In Proc. American Control Conf. 2007, 3112–3117, New York, NY, 2007.
- F. M. Atay and A. Hutt. Neural fields with distributed transmission speeds and long-range feedback delays. SIAM J. Appl. Dynamical Systems 5:670–698, 2006.
- F. M. Atay, T. Biyikoglu, and J. Jost. Network synchronization: Spectral versus statistical properties. Physica D 224:35–41, 2006.
- F. M. Atay and O. Karabacak. Stability of coupled map networks with delays. SIAM J. Appl. Dynamical Systems 5:508–527, 2006.
- S. Jalan, J. Jost, and F. M. Atay. Symbolic synchronization and the detection of global properties of coupled dynamics from local information. Chaos 16:033124, 2006.
- F. M. Atay. Oscillator death in coupled functional differential equations near Hopf bifurcation. J. Differential Equations 221(1):190–209, 2006.
- A. Hutt and F. M. Atay. Effects of distributed transmission speeds on propagating activity in neural populations. Physical Review E 73(2):021906, 2006.
- F. M. Atay, T. Biyikoglu, and J. Jost. Synchronization of networks with prescribed degree distributions. IEEE Trans. Circuits and Systems I, 53(1):92–98, 2006.
- F. M. Atay and A. Hutt. Stability and bifurcations in neural fields with finite propagation speed and general connectivity. SIAM J. Applied Math. 65(2):644–666, 2005.
- F. M. Atay and T. Biyikoglu. Graph operations and synchronization of complex networks. Physical Review E 72:016217, 2005.
- A. Hutt and F. M. Atay. Analysis of nonlocal neural fields for both general and gamma-distributed connectivities. Physica D 203(1–2):30–54, 2005.
- F. M. Atay. Stability of coupled delay differential equations near Hopf bifurcation. In Proc. EQUADIFF 2003: International Conference on Differential Equations (F. Dumortier et al., ed.), 1027–1030, Hasselt, Belgium, 2003 (World Scientific, 2005).
- F. M. Atay and J. Jost. Kopplung von Dynamiken und Strukturbildung.
In Max-Planck-Gesellschaft: Jahrbuch 2005, p. 375–378, Max-Planck-Gesellschaft, Muenchen, 2005.
- F. M. Atay, J. Jost, and A. Wende. Delays, connection topology, and synchronization of coupled chaotic maps. Physical Review Letters 92(14):144101, 2004.
- F. M. Atay and J. Jost. On the emergence of complex systems on the basis of the coordination of complex behaviors of their elements. Complexity 10(1):17–22, 2004.
- F. M. Atay. Distributed delays facilitate amplitude death of coupled oscillators. Physical Review Letters 91(9):094101, 2003.
- F. M. Atay. Total and partial amplitude death in networks of diffusively coupled oscillators. Physica D 183(1–2):1–18, 2003.
- F. M. Atay. Synchronization and death in delay-coupled van der Pol oscillators.In Proc. NDES 2003: The 11th Workshop on Nonlinear Dynamics of Electronic Systems (R. Stoop, ed.), 21–24, Scuol, Switzerland, 2003.
- F. M. Atay. Delayed-feedback control of oscillations in non-linear planar systems. Int. J. Control 75(5):297–304, 2002.
- F. M. Atay. Oscillation control in delayed feedback systems. In Dynamics, Bifurcations, and Control (F. Colonius, L. Grüne, eds.), Lect. Notes in Control and Information Sciences 273:103–116, 2002.
- F. M. Atay. Partial amplitude death in diffusively coupled oscillators. In Proc. NDES 2002: The 10th Workshop on Nonlinear Dynamics of Electronic Systems, 4:5–8, Cesme, Turkey, 2002.
- U. Erdemir, U. Tekin, F. M. Atay, and A. Ercil. Two-dimensional object recognition using power spectrum. In Proc. SIU 2002: The 10th Congress on Signal Processing and Applications (E. Panayirci, ed.), Vol. 2, 1044–1049, Pamukkale, Turkey, 2002.
- F. M. Atay. Periodic solutions of delay-differential equations with a restorative condition. Nonlinear Analysis TMA 45(5):555–576, 2001.
- F. M. Atay, T. Durakbasa, A. Duyar. A novel method for fault detection in electrical motors. Sound and Vibration 35(2):26–29, 2001.
- F. M. Atay. Magnetic saturation and steady-state analysis of electrical motors. Applied Math. Modelling 24(11):827–842, 2000.
- E. Albas, V. Eldem, and F. M. Atay. Identification of compressor faults through model based fault detection approach. In Proc. 2000 International Compressor Engineering Conference at Purdue (W. Soedel, ed.), 539–546, Purdue University, West Lafayette, IN, 2000.
- F. M. Atay and Y. Altintas. Recovering smooth dynamics from time series with the aid of recurrence plots. Physical Review E 59(6):6593–6598, 1999.
- F. M. Atay. Balancing the inverted pendulum using position feedback. Applied Math. Letters 12:51–56, 1999.
- F. M. Atay, E. Albas, and V. Eldem. Modelling and identification of saturation in electrical machinery. In Integrating Dynamics, Condition Monitoring and Control for the 21st Century (A. G. Starr et al., eds.), 343–347, A. A. Balkema, Rotterdam, 1999.
- F. M. Atay, E. Albas, Y. Aktunc, and T. Durakbasa. Development of a model-based fault detection system for electrical motors. Otomasyon 86:26–29, 1999.
- F. M. Atay and J. Mallet-Paret. Modeling reflex asymmetries with implicit delay differential equations. Bull. Math. Biology 60(6):999–1015, 1998.
- F. M. Atay. Van der Pol’s oscillator under delayed feedback. J. Sound and Vibration 218(2):333–339, 1998.
- F. M. Atay and E. Yurtsever. Phase-space reconstruction in Hamiltonian systems through multiple time series. Chemical Physics Letters 276(3-4):282–288, 1997.
- A. Sennaroglu, F. M. Atay, and A. Askar. Laser beam propagation in a saturable absorber. J. Optical Society of America B 14(10):2577–2583, 1997.
- A. Sennaroglu, A. Askar, and F. M. Atay. A quantitative study of laser beam propagation in a thermally loaded absorber. J. Optical Society of America B 14(2):356–363, 1997.
- F. M. Atay. Stability, feedback, and delays. In Proc. 15th International System Dynamics Conference (Y. Barlas, V. G. Diker, and S. Polat, eds.), 699–702, Istanbul, Turkey, 1997.
- A. Sennaroglu, A. Askar, and F. M. Atay. Laser beam propagation in a thermally loaded absorber. In OSA TOPS on Advanced Solid-State Lasers (S.A. Payne and C. Pollock, eds.), Vol. 1, 222–226. Optical Society of America, Washington D.C., 1996.
- A. Sennaroglu, A. Askar, and F. M. Atay. Laser beam propagation in a thermally loaded absorber. In Advanced Solid-State Lasers, 1996 Technical Digest, 418–420. Optical Society of America, Washington D.C., 1996.
- F. M. Atay. A stabilizing mechanism in the pupil light reflex.
In COMCON 5: The 5th International Conference on Advances in Communication and Control (W. Wells, ed.), 853–857, Crete, Greece, 1996.
- F. M. Atay. A differential-delay equation arising in the modelling of the pupil light reflex. Ph.D. Thesis, Brown University, RI, 1994.
- F. M. Atay and K. Ozcaldiran. Reachability and controllability subspaces for singular systems: A matrix pencil characterization. In Realization and Modelling in System Theory (M. A. Kaashoek, J. H. Van Schuppen, and A. C. M. Ran, eds.), Vol. 1, 241–246. Birkhäuser Boston, 1990.
- F. M. Atay. A characterization of the reachability subspaces of singular systems through matrix pencils. M.S. Thesis, Bogazici University, Istanbul, 1989.