Global phase-locking in finite populations of phase-coupled oscillators

We present new necessary and sufficient conditions for the existence of fixed points in a finite system of coupled phase oscillators on a complete graph. We use these conditions to derive bounds on the critical coupling.Comment: 31 pages; to appear in SIAM journal of dynamical systems (SIADS

Synchronisation effects on the behavioural performance and information dynamics of a simulated minimally cognitive robotic agent

Oscillatory activity is ubiquitous in nervous systems, with solid evidence that synchronisation mechanisms underpin cognitive processes. Nevertheless, its informational content and relationship with behaviour are still to be fully understood. In addition, cognitive systems cannot be properly appreciated without taking into account brain–body– environment interactions. In this paper, we developed a model based on the Kuramoto Model of coupled phase oscillators to explore the role of neural synchronisation in the performance of a simulated robotic agent in two different minimally cognitive tasks. We show that there is a statistically significant difference in performance and evolvability depending on the synchronisation regime of the network. In both tasks, a combination of information flow and dynamical analyses show that networks with a definite, but not too strong, propensity for synchronisation are more able to reconfigure, to organise themselves functionally and to adapt to different behavioural conditions. The results highlight the asymmetry of information flow and its behavioural correspondence. Importantly, it also shows that neural synchronisation dynamics, when suitably flexible and reconfigurable, can generate minimally cognitive embodied behaviour

Stability of an [N/2]-dimensional invariant torus in the Kuramoto model at small coupling

When the natural frequencies are allocated symmetrically in the Kuramoto model there exists an invariant torus of dimension [N/2]+1 (N is the population size). A global phase shift invariance allows to reduce the model to $N-1$ dimensions using the phase differences, and doing so the invariant torus becomes [N/2]-dimensional. By means of perturbative calculations based on the renormalization group technique, we show that this torus is asymptotically stable at small coupling if N is odd. If N is even the torus can be stable or unstable depending on the natural frequencies, and both possibilities persist in the small coupling limit.Comment: to appear in Physica

Neuronal oscillations, information dynamics, and behaviour: an evolutionary robotics study

Oscillatory neural activity is closely related to cognition and behaviour, with synchronisation mechanisms playing a key role in the integration and functional organization of different cortical areas. Nevertheless, its informational content and relationship with behaviour - and hence cognition - are still to be fully understood. This thesis is concerned with better understanding the role of neuronal oscillations and information dynamics towards the generation of embodied cognitive behaviours and with investigating the efficacy of such systems as practical robot controllers. To this end, we develop a novel model based on the Kuramoto model of coupled phase oscillators and perform three minimally cognitive evolutionary robotics experiments. The analyses focus both on a behavioural level description, investigating the robot’s trajectories, and on a mechanism level description, exploring the variables’ dynamics and the information transfer properties within and between the agent’s body and the environment. The first experiment demonstrates that in an active categorical perception task under normal and inverted vision, networks with a definite, but not too strong, propensity for synchronisation are more able to reconfigure, to organise themselves functionally, and to adapt to different behavioural conditions. The second experiment relates assembly constitution and phase reorganisation dynamics to performance in supervised and unsupervised learning tasks. We demonstrate that assembly dynamics facilitate the evolutionary process, can account for varying degrees of stimuli modulation of the sensorimotor interactions, and can contribute to solving different tasks leaving aside other plasticity mechanisms. The third experiment explores an associative learning task considering a more realistic connectivity pattern between neurons. We demonstrate that networks with travelling waves as a default solution perform poorly compared to networks that are normally synchronised in the absence of stimuli. Overall, this thesis shows that neural synchronisation dynamics, when suitably flexible and reconfigurable, produce an asymmetric flow of information and can generate minimally cognitive embodied behaviours