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Fox JJ, Jayaprakash C, Wang D, Campbell SR. Synchronization in Relaxation Oscillator Networks with Conduction Delays. Neural Comput 2001; 13:1003-21. [PMID: 11359642 DOI: 10.1162/08997660151134307] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
Abstract
We study locally coupled networks of relaxation oscillators with excitatory connections and conduction delays and propose a mechanism for achieving zero phase-lag synchrony. Our mechanism is based on the observation that different rates of motion along different nullclines of the system can lead to synchrony in the presence of conduction delays. We analyze the system of two coupled oscillators and derive phase compression rates. This analysis indicates how to choose nullclines for individual relaxation oscillators in order to induce rapid synchrony. The numerical simulations demonstrate that our analytical results extend to locally coupled networks with conduction delays and that these networks can attain rapid synchrony with appropriately chosen nullclines and initial conditions. The robustness of the proposed mechanism is verified with respect to different nullclines, variations in parameter values, and initial conditions.
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Chen K, Ebner C, Jayaprakash C, Pandit R. Micro-emulsions in oil-water-surfactant mixtures: an Ising lattice gas model. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0022-3719/20/17/001] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Campbell SR, Wang DL, Jayaprakash C. Synchrony and desynchrony in integrate-and-fire oscillators. Neural Comput 1999; 11:1595-619. [PMID: 10490940 DOI: 10.1162/089976699300016160] [Citation(s) in RCA: 125] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
Abstract
Due to many experimental reports of synchronous neural activity in the brain, there is much interest in understanding synchronization in networks of neural oscillators and its potential for computing perceptual organization. Contrary to Hopfield and Herz (1995), we find that networks of locally coupled integrate-and-fire oscillators can quickly synchronize. Furthermore, we examine the time needed to synchronize such networks. We observe that these networks synchronize at times proportional to the logarithm of their size, and we give the parameters used to control the rate of synchronization. Inspired by locally excitatory globally inhibitory oscillator network (LEGION) dynamics with relaxation oscillators (Terman & Wang, 1995), we find that global inhibition can play a similar role of desynchronization in a network of integrate-and-fire oscillators. We illustrate that a LEGION architecture with integrate-and-fire oscillators can be similarly used to address image analysis.
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Hayot F, Jayaprakash C. Multifractality in the stochastic Burgers equation. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:4681-4684. [PMID: 9965646 DOI: 10.1103/physreve.54.4681] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Chen K, Jayaprakash C. X-ray-edge singularities with nonconstant density of states: A renormalization-group approach. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:14436-14440. [PMID: 9980774 DOI: 10.1103/physrevb.52.14436] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Bohr T, Grinstein G, Jayaprakash C. Singular Lyapunov spectra and conservation laws. CHAOS (WOODBURY, N.Y.) 1995; 5:412-415. [PMID: 12780194 DOI: 10.1063/1.166111] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We give analytic arguments and numerical evidence to show that the presence of conservation laws can produce a singularity in the spectrum of Lyapunov exponents for extended dynamical systems of low spatial dimensionality. This phenomenon can be used, e.g., for finding hidden conservation laws. (c) 1995 American Institute of Physics.
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Hu F, Sarker SK, Jayaprakash C. Domain walls, spiral states, and phase separation in the extended Hubbard model: A Hartree-Fock analysis. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:17901-17909. [PMID: 9976223 DOI: 10.1103/physrevb.50.17901] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Grinstein G, Jayaprakash C, Bennett CH. Comment on "Second-order dynamics in the collective temporal evolution of complex systems". PHYSICAL REVIEW LETTERS 1994; 73:3038. [PMID: 10057266 DOI: 10.1103/physrevlett.73.3038] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Bhagavatula R, Ebner C, Jayaprakash C. Spatiotemporal chaos in Josephson-junction arrays. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:9376-9379. [PMID: 9974986 DOI: 10.1103/physrevb.50.9376] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Bhagavatula R, Chen K, Jayaprakash C, Xu HJ. Green's function method for random fuse network problems. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 49:5001-5006. [PMID: 9961820 DOI: 10.1103/physreve.49.5001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Jayaprakash C, Hayot F, Pandit R. Jayaprakash, Hayot, and Pandit reply. PHYSICAL REVIEW LETTERS 1994; 72:308. [PMID: 10056114 DOI: 10.1103/physrevlett.72.308] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Bhagavatula R, Jayaprakash C. Non-Gaussian distributions in extended dynamical systems. PHYSICAL REVIEW LETTERS 1993; 71:3657-3660. [PMID: 10055039 DOI: 10.1103/physrevlett.71.3657] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Grinstein G, Jayaprakash C, Socolar JE. Scale invariance of nonconserved quantities in driven systems. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 48:R643-R646. [PMID: 9960763 DOI: 10.1103/physreve.48.r643] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Jayaprakash C, Hayot F, Pandit R. Universal properties of the two-dimensional Kuramoto-Sivashinsky equation. PHYSICAL REVIEW LETTERS 1993; 71:12-15. [PMID: 10054360 DOI: 10.1103/physrevlett.71.12] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Socolar JE, Grinstein G, Jayaprakash C. On self-organized criticality in nonconserving systems. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 47:2366-2376. [PMID: 9960267 DOI: 10.1103/physreve.47.2366] [Citation(s) in RCA: 75] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Hayot F, Jayaprakash C, Josserand C. Long-wavelength properties of the Kuramoto-Sivashinsky equation. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 47:911-915. [PMID: 9960085 DOI: 10.1103/physreve.47.911] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Sneppen K, Krug J, Jensen MH, Jayaprakash C, Bohr T. Dynamic scaling and crossover analysis for the Kuramoto-Sivashinsky equation. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 46:R7351-R7354. [PMID: 9908164 DOI: 10.1103/physreva.46.r7351] [Citation(s) in RCA: 55] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Bhagavatula R, Grinstein G, He Y, Jayaprakash C. Algebraic correlations in conserving chaotic systems. PHYSICAL REVIEW LETTERS 1992; 69:3483-3486. [PMID: 10046833 DOI: 10.1103/physrevlett.69.3483] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Bohr T, Grinstein G, Jayaprakash C, Jensen MH, Mukamel D. Chaotic interface dynamics: A model with turbulent behavior. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 46:4791-4796. [PMID: 9908698 DOI: 10.1103/physreva.46.4791] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Chen K, Jayaprakash C, Krishnamurthy HR. Spatially dependent zero-frequency response functions and correlation functions in the Kondo model. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 45:5368-5386. [PMID: 10000254 DOI: 10.1103/physrevb.45.5368] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Bhagavatula R, Ebner C, Jayaprakash C. Dynamics of capacitive Josephson-junction arrays subjected to electromagnetic radiation. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 45:4774-4787. [PMID: 10002115 DOI: 10.1103/physrevb.45.4774] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Grinstein G, He Y, Jayaprakash C, Bolker B. Collective behavior of a coupled-map system with a conserved quantity. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1991; 44:4923-4936. [PMID: 9906544 DOI: 10.1103/physreva.44.4923] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Wenzel W, Biham O, Jayaprakash C. Periodic orbits in the dissipative standard map. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1991; 43:6550-6557. [PMID: 9905005 DOI: 10.1103/physreva.43.6550] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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50
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Sarker S, Jayaprakash C, Krishnamurthy HR, Wenzel W. Spiral states in the square-lattice Hubbard model. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 43:8775-8778. [PMID: 9996544 DOI: 10.1103/physrevb.43.8775] [Citation(s) in RCA: 24] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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