Signal processing in coupled stochastic systems

JORDI GARCIA OJALVO; PABLO BALENZUELA; JAVIER MARTIN BULDU; CRISTINA MARTINEZ; M. CARME TORRENT

Berlin, Alemania

Congreso; Dynamics Days 2005; 2005

Technische Universitat Berlin, Germany

Networks of dynamical systems are frequently involved in the detection and processing of complex signals. An important example is provided by networks of neurons in many multicellular organisms, which must be able to monitor a complex environment in a reliable way, even in the presence of a substantial amount of noise acting within the internal environment of the system (i.e. the neural tissue itself ). In order to investigate how coupled excitable elements in the presence of noise are able to process complex signals, we consider simple systems of two coupled elements sub ject to the simplest nontrivial signal, namely a complex harmonic driving com- posed of a series of harmonics in which the fundamental is absent. In the presence of this type of signal, excitable systems are able to detect the fundamental frequency, in what is known as the “missing fundamental illusion”. Recently a mechanism for this phenomenon has been proposed on the basis of the so-called ghost stochas- tic resonance [1]; this mechanism has been verified experimentally in an excitable semiconductor laser [2]. We have investigated how the missing fundamental originates not at the detec- tion, but at the processing level, by using a complex harmonic signal in which the harmonics are distributed among the different coupled elements. In this case, cou- pling is seen to mediate the processing of the signal and the subsequent generation of the missing fundamental. Two different coupling architectures will be discussed: two excitable units coupled bidirectionally by mutual injection, and a neuronal net- work composed of two sensory neurons acting synaptically (and unidirectionally) upon a third processing neuron. The former situation has been analyzed experimen- tally in systems of coupled semiconductor lasers operating in an excitable regime [3]; the latter provides an explanation [4] for the binaural perception of pitch reported experimentally in the human brain [5]. [1] D. R. Chialvo, O. Calvo, D. L. Gonzalez, O. Piro, and G. V. Savino, Phys. Rev. E 65, 050902(R) (2002). [2] J.M. Buld ́u, D.R. Chialvo, C.R. Mirasso, M.C. Torrent, and J. Garc ́ıa-Ojalvo, Europhys. Lett. 64, 178 (2003). [3] J. M. Buldu, C. M. Gonzalez, J. Trull, M. C. Torrent, and J. Garcia-Ojalvo, Chaos 15, 013103 (2005). [4] P. Balenzuela and J. Garcia-Ojalvo, Chaos, in press (2005). [5] C. Pantev, T. Elbert, B. Ross, C. Eulitz, E. Terhardt, Hearing Research 100, 164 (1996).