We design a high efficient exponential time differencing method (ETD) for simulating pulse-coupled Hodgkin-Huxley (HH) neuronal networks. The ETD method is attractive because it can solve the stiff problem when a HH neuron fires a spike and allows a large time step to raise efficiency . For pulse-coupled HH networks, the synaptic spike times are unknown before evolving. We have to evolve the network without considering them and carefully assign them at the end of time step to achieve a second-order accuracy. We find that the second-order ETD method with Runge-Kutta time stepping (ETD2RK) is less accurate than the second-order Runge-Kutta method (RK2) using a common time step. Besides, we observe that the HH equations are quite flat outside the stiff period where RK2 method also allows a large time step. Thus, we adaptively assign the ETD2RK and RK2 schemes depending on the stiff and flat regimes to achieve optimal accuracy and efficiency . Compared with the regular RK2 method , our ETD2RK method can enlarge time steps and raise efficiency more than one order of magnitude while capturing excellent accurate traces of membrane potentials and spike times of HH neurons. This high accuracy and efficiency can be robustly obtained without relying on the dynamical regimes, structural connectivity or the scale of networks .
The exponential time differencing (ETD) method allows using a large time step to efficiently evolve the stiff system such as Hodgkin-Huxley (HH) neural networks . For pulse-coupled HH networks, the synaptic spike times cannot be predetermined and are convoluted with neuron's trajectory itself. This presents a challenging issue for the design of an efficient numerical simulation algorithm. The stiffness in the HH equations are quite different between the spike and non-spike regions. Here, we design a second-order adaptive exponential time differencing algorithm (AETD2) for the numerical evolution of HH neural networks . Compared with the regular second-order Runge-Kutta method (RK2), our AETD2 method can use time steps one order of magnitude larger and improve computational efficiency more than ten times while excellently capturing accurate traces of membrane potentials of HH neurons. This high accuracy and efficiency can be robustly obtained and do not depend on the dynamical regimes, connectivity structure or the network size .
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We design a high efficient
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method
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for simulating pulse-coupled Hodgkin-Huxley (HH) neuronal networks. The ETD method is attractive because it can solve the stiff problem when a HH neuron fires a spike and allows
method allows using
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raise efficiency
efficiently evolve the stiff system such as Hodgkin-Huxley (HH) neural networks
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are unknown before evolving. We have to evolve the network without considering them and carefully assign them at the end of time step to achieve a second-order accuracy. We find that the second-order ETD method with Runge-Kutta time stepping (ETD2RK) is less accurate than the second-order Runge-Kutta method (RK2) using a common time step. Besides, we observe that the
cannot be predetermined and are convoluted with neuron's trajectory itself. This presents a challenging issue for the design of an efficient numerical simulation algorithm. The stiffness in the
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flat outside the stiff period where RK2 method also allows a large time step. Thus, we adaptively assign the ETD2RK and RK2 schemes depending on the stiff and flat regimes to achieve optimal accuracy and efficiency
different between the spike and non-spike regions. Here, we design a second-order adaptive exponential time differencing algorithm (AETD2) for the numerical evolution of HH neural networks
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RK2 method , our ETD2RK method can enlarge time steps and raise efficiency more than
second-order Runge-Kutta method (RK2), our AETD2 method can use time steps
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while capturing excellent
larger and improve computational efficiency more than ten times while excellently capturing
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and spike times
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without relying
and do not depend
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structural connectivity or the scale of networks
connectivity structure or the network size