Collective Modes in Neural Nets and their Dissipative Dynamics

Abstract Walter Freeman’s mesoscopic neurodynamics placed a fundamental problemat the center of brain science, i.e. how local neural activity gives rise to coherentorganization at the scale of whole populations. Here we explore this problemby means of a finite dissipative neural field model. Starting from an initiallyunbiased lattice of interacting complex SU(2) doublets, a transient externalinput drives the network toward a stable macroscopic order. After the inputis removed, the neural field continues to reorganize spontaneously aroundthe established order, while coordinated fluctuations and spatial patternsemerge across distant regions of the lattice. These features provide finite-sizesignatures of the same organizing principles that, in Quantum Field Theory, areassociated with spontaneous symmetry breaking and collective modes. Importantly, theyappear in a finite system, without requiring the thermodynamic limit. Suchfinite neural fields therefore offer not only a bridge between local dynamicsand collective organization, but also a computational tool for developing andtesting new hypotheses about brain function.