# Synchronization dynamics of two coupled neural oscillators receiving shared and unshared noisy stimuli

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## Abstract

The response of neurons to external stimuli greatly depends on the intrinsic dynamics of the network. Here, the intrinsic dynamics are modeled as coupling and the external input is modeled as shared and unshared noise. We assume the neurons are repetitively firing action potentials (i.e., neural oscillators), are weakly and identically coupled, and the external noise is weak. Shared noise can induce bistability between the synchronous and anti-phase states even though the anti-phase state is the only stable state in the absence of noise. We study the Fokker-Planck equation of the system and perform an asymptotic reduction *ρ* _{0}. The *ρ* _{0} solution is more computationally efficient than both the Monte Carlo simulations and the 2D Fokker-Planck solver, and agrees remarkably well with the full system with weak noise and weak coupling. With moderate noise and coupling, *ρ* _{0} is still qualitatively correct despite the small noise and coupling assumption in the asymptotic reduction. Our phase model accurately predicts the behavior of a realistic synaptically coupled Morris-Lecar system.

## Keywords

Neural oscillators Shared noise Weak coupling Weak noise Bistability## Notes

### Acknowledgements

We thank Brent Doiron for useful discussions. CL is supported by an NSF Postdoctoral Fellowship # DMS0703502. GBE is supported by an NSF grant # DMS0513500.

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