Stochastic resonance in coupled threshold elements on a Barabási–Albert network

Stochastic resonance is investigated in a system of threshold elements located at nodes and coupled along edges of a Barabasi–Albert network, driven by a common subthreshold periodic signal and independent noises. Array-enhanced stochastic resonance is observed, i.e., increase of the spectral power amplification evaluated from the mean output of the network due to proper coupling. This enhancement occurs though the response of individual threshold elements to the periodic signal is very diverse due to a power-law distribution of their connectivity. Numerical results are qualitatively explained using simple linear response theory in the mean field approximation.

[1]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[2]  Moshe Gitterman,et al.  Small-world phenomena in physics: the Ising model , 2000 .

[3]  Response in kinetic Ising model to oscillating magnetic fields , 1998, cond-mat/9804251.

[4]  Bulsara,et al.  Array enhanced stochastic resonance and spatiotemporal synchronization. , 1995, Physical review letters.

[5]  Nigel G. Stocks,et al.  STOCHASTIC RESONANCE IN MONOSTABLE SYSTEMS , 1993 .

[6]  Jung,et al.  Amplification of small signals via stochastic resonance. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[7]  S. Redner,et al.  Connectivity of growing random networks. , 2000, Physical review letters.

[8]  Lutz Schimansky-Geier,et al.  Analytical study of coupled two-state stochastic resonators , 1998 .

[9]  A. Pekalski,et al.  Ising model on a small world network. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Bulsara,et al.  Scaling laws for spatiotemporal synchronization and array enhanced stochastic resonance. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  A. Sutera,et al.  The mechanism of stochastic resonance , 1981 .

[12]  Gang Hu,et al.  Stochastic resonance of small-world networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  G. A. Johnson,et al.  Stochastic resonance in coupled nonlinear dynamic elements. , 1998, Chaos.

[14]  Bulsara,et al.  Nonlinear dynamic elements with noisy sinusoidal forcing: Enhancing response via nonlinear coupling. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[15]  D. Zanette,et al.  Stochastic resonance in a model of opinion formation on small-world networks , 2001, cond-mat/0111289.

[16]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[17]  Frank Moss.  Self-Organized Biological Dynamics and Nonlinear Control: Stochastic resonance: looking forward , 2000 .

[18]  Chapeau-Blondeau.  Stochastic resonance in the Heaviside nonlinearity with white noise and arbitrary periodic signal. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  Wiesenfeld,et al.  Theory of stochastic resonance. , 1989, Physical review. A, General physics.

[20]  X. Yang,et al.  Chaos in small-world networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Jung,et al.  Collective response in globally coupled bistable systems. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[22]  S. N. Dorogovtsev,et al.  Structure of growing networks with preferential linking. , 2000, Physical review letters.

[23]  Wiesenfeld,et al.  Stochastic resonance on a circle. , 1994, Physical review letters.

[24]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[25]  G. Bianconi.  Mean field solution of the Ising model on a Barabási–Albert network , 2002, cond-mat/0204455.

[26]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[27]  François Chapeau-Blondeau,et al.  STOCHASTIC RESONANCE IN NONLINEAR TRANSMISSION OF SPIKE SIGNALS: AN EXACT MODEL AND AN APPLICATION TO THE NEURON , 1996 .

[28]  Toru Ohira,et al.  Delayed stochastic resonance with a 1-D ring , 2002 .

[29]  Wei Wang,et al.  Frequency sensitivity in weak signal detection , 1999 .

[30]  Beom Jun Kim,et al.  Stochastic resonance in the driven Ising model on small-world networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  W. Ditto,et al.  Monostable array-enhanced stochastic resonance. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Frank Moss,et al.  Stochastic resonance: noise-enhanced order , 1999 .

[33]  Xiao Fan Wang,et al.  Synchronization in scale-free dynamical networks: robustness and fragility , 2001, cond-mat/0105014.

[34]  Kosiński,et al.  Stochastic resonance and noise-enhanced order with spatiotemporal periodic signal , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[35]  Reka Albert,et al.  Mean-field theory for scale-free random networks , 1999 .

[36]  F. Moss,et al.  Non-Dynamical Stochastic Resonance: Theory and Experiments with White and Arbitrarily Coloured Noise , 1995 .

[37]  D. Stauffer,et al.  Ferromagnetic phase transition in Barabási–Albert networks , 2001, cond-mat/0112312.