Microscopic mechanism for self-organized quasiperiodicity in random networks of nonlinear oscillators.
Self-organized quasiperiodicity is one of the most puzzling dynamical phases observed in systems of nonlinear coupled oscillators. The single dynamical units are not locked to the periodic mean field they produce, but they still feature a coherent behavior, through an unexplained complex form of correlation. We consider a class of leaky integrate-and-fire oscillators on random sparse and massive networks with dynamical synapses, featuring self-organized quasiperiodicity, and we show how complex collective oscillations arise from constructive interference of microscopic dynamics. In particular, we find a simple quantitative relationship between two relevant microscopic dynamical time scales and the macroscopic time scale of the global signal. We show that the proposed relation is a general property of collective oscillations, common to all the partially synchronous dynamical phases analyzed. We argue that an analogous mechanism could be at the origin of similar network dynamics.
Dipartimento di Fisica e Scienza della Terra, Università di Parma, via G. P. Usberti, 7/A 43124, Parma, Italy and INFN, Gruppo Collegato di Parma, via G. P. Usberti, 7/A 43124, Parma, Italy.
Raffaella
R
Burioni
Dipartimento di Fisica e Scienza della Terra, Università di Parma, via G. P. Usberti, 7/A 43124, Parma, Italy.
Serena
S
di Santo
Dipartimento di Fisica e Scienza della Terra, Università di Parma, via G. P. Usberti, 7/A 43124, Parma, Italy and INFN, Gruppo Collegato di Parma, via G. P. Usberti, 7/A 43124, Parma, Italy and Centro Interdipartimentale per lo Studio delle Dinamiche Complesse, via Sansone, 1 50019 Sesto Fiorentino, Italy.
Matteo
M
di Volo
Dipartimento di Fisica e Scienza della Terra, Università di Parma, via G. P. Usberti, 7/A 43124, Parma, Italy and S3, CNR Istituto di Nanoscienze, Via Campi, 213A 41125 Modena, Italy.
Alessandro
A
Vezzani
D005583:Fourier Analysis; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics; D010507:Periodicity