BB8: Mathematical models of spatially coherent brain states

Project report to follow

Background

The synchronisation of oscillating systems has been studied in various contexts. In ecology, synchronisation of a metapopulation, or an ensemble of spatially separated populations, is particularly important. This is because synchronisation is correlated with the likelihood of global extinction, which may be desirable, for example in pathogen control, or undesirable, for example in conservation of endangered species.

Techniques and Challenges

Our research has focused on the effects of noise on synchronisation in two contexts: columns of neurons and populations of organisms. Due to the interactions of inhibitory and excitatory neurons in the former, and predators and prey in the latter, we see large-scale limit cycle oscillations in these systems. This allows us to apply the theories of stochastic phase reduction, averaging and noise-induced synchronisation to study the interactions between different types of noise – correlated noise tends to synchronise systems, and uncorrelated noise tends to desynchronise systems. We have also compared our analysis to various numerical simulations, such as Monte Carlo methods.

Results

We have applied the techniques above to an ecological system and have shown that noise-induced synchronisation of limit cycle oscillators can be used as an explanation for the long-known Moran effect, where spatially isolated patches of organisms are driven by a global extrinsic noise source, such as weather conditions. One major implication of our work is that the stabilising effects of demographic noise could provide an explanation for why oscillations are often not observed in real ecological systems, in contrast to predictions of deterministic models.

The Future

We are pursuing an extremely promising avenue of research by considering the effects of coupling between oscillators in particular, dispersal in ecological models. Depending on the system, dispersal can cause synchrony as well as phase-locked asynchronous states. This then displays extremely interesting behaviour when noise is introduced.

References

[12/38] Bressloff P.C., Lai Y.M.: Dispersal and noise: various modes of synchrony in ecological oscillators

[11/47] Lai Y.M., Newby J., Bressloff P.C.: Effects of demographic noise on the synchronization of a metapopulation in a fluctuating environment, Physical Review Letters

[10/60] Bressloff P.C., Lai Y.M.: Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise, Journal Mathematical Neuroscience