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math.DS2020
Analysis of Neural Clusters due to Deep Brain Stimulation Pulses
Daniel Kuelbs, Jacob Dunefsky, Bharat Monga +1
Deep brain stimulation (DBS) is an established method for treating pathological conditions such as Parkinson's disease, dystonia, Tourette syndrome, and essential tremor. While the…
math.DS2020
Augmented Phase Reduction for Periodic Orbits Near a Homoclinic Bifurcation and for Relaxation Oscillators
Bharat Monga, Jeff Moehlis
Oscillators - dynamical systems with stable periodic orbits - arise in many systems of physical, technological, and biological interest. The standard phase reduction, a model reduc…
math.DS2013★ 208 cited
Isostables, isochrons, and Koopman spectrum for the action-angle representation of stable fixed point dynamics
Alexandre Mauroy, Igor Mezic, Jeff Moehlis
For asymptotically periodic systems, a powerful (phase) reduction of the dynamics is obtained by computing the so-called isochrons, i.e. the sets of points that converge toward the…