2 research outputs found
Fractional Schr\"odinger equation and time dependent potentials
We investigate the solutions for a time dependent potential by considering
two scenarios for the fractional Schr\"odinger equation. The first scenario
analyzes the influence of the time dependent potential in the absence of the
kinetic term. We obtain analytical and numerical solutions for this case by
considering the Caputo fractional time derivative, which extends Rabi's model.
In the second scenario, we incorporate the kinetic term in the Schr\"odinger
equation and consider fractional spatial derivatives. For this case, we analyze
the spreading of the Gaussian wave package under the action of the time and
spatial fractional differential operators
Noise induces continuous and noncontinuous transitions in neuronal interspike intervals range
Noise appears in the brain due to various sources, such as ionic channel fluctuations and synaptic events. They affect the activities of the brain and influence neuron action potentials. Stochastic differential equations have been used to model firing patterns of neurons subject to noise. In this work, we consider perturbing noise in the adaptive exponential integrate-and-fire (AEIF) neuron. The AEIF is a two- dimensional model that describes different neuronal firing patterns by varying its parameters. Noise is added in the equation related to the membrane potential. We show that a noise current can induce continuous and noncontinuous transitions in neuronal interspike intervals. Moreover, we show that the noncontinuous transition occurs mainly for parameters close to the border between tonic spiking and burst activities of the neuron without nois