Networks in the brain consist of different types of neurons. We here investigate the influence of neuron diversity on the dynamical stability , phase space structure , and computational capabilities of inhibitory spiking networks using mixtures of neurons with positive and negative dissipation . We find that already a single neuron of a different type may qualitatively change the dynamics of a neural network and that mixed networks can combine the computational capabilities of ones with only a single neuron type. Our networks contain leaky integrate-and-fire neurons (positive dissipation) as well as neurons with inverted sign of the leak current (negative dissipation) . We first show that such networkscan exhibit a balanced state of irregular , asynchronous spiking activity, if the neurons with negative dissipation are endowed with a voltage-dependent input cutoff, which may be interpreted as a simple conductance-based implementation of their synapses. We compute the voltage probability distributions and self-consistent firing rates for both types of neurons for finite size spike impacts assuming that inputs are Poissonian. The balanced state exists in a variety of neural network models and its dynamical properties such as chaoticity vary considerably. Our models generalize networks of leaky integrate-and-fire neurons where the dynamics are non-chaotic despite their irregularity. We show that switching the sign of the dissipation of a single neuron renders the entire network dynamics unstable and chaotic as indicated by a positive largest Lyapunov exponent. To further characterize the dynamics we consider the full spectrum of Lyapunov exponents and the related covariant Lyapunov vectors (CLVs) , which indicate the directions in which infinitesimal perturbations grow or shrink with a rate given by the Lyapunov exponents . We find that for each .. .
Networks in the brain consist of different types of neurons. Here we investigate the influence of neuron diversity on the dynamics , phase space structure and computational capabilities of spiking neural networks . We find that already a single neuron of a different type can qualitatively change the network dynamics and that mixed networks may combine the computational capabilities of ones with a single neuron type. We study inhibitory networks of concave leaky (LIF) and convex "anti-leaky" (XIF) integrate-and-fire neurons that generalize irregularly spiking non-chaotic LIF neuron networks. Endowed with simple conductance-based synapses for XIF neurons, our networks can generate a balanced state of irregular asynchronous spiking as well. We determine the voltage probability distributions and self-consistent firing rates assuming Poisson input with finite size spike impacts . Further, we compute the full spectrum of Lyapunov exponents (LEs) and the covariant Lyapunov vectors (CLVs) specifying the corresponding perturbation directions . We find that there is approximately one positive LE for each XIF neuron. This indicates in particular that a single XIF neuron renders the network dynamics chaotic. A simple mean-field approach, which can be justified by properties of the CLVs, explains the finding. As an application, we propose a spike-based computing scheme where our networks serve as computational reservoirs and their different stability properties yield different computational capabilities .
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dynamical stability
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inhibitory spiking networks using mixtures of neurons with positive and negative dissipation
spiking neural networks
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dynamics of a neural network
network dynamics
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Our networks contain leaky
We study inhibitory networks of concave leaky (LIF) and convex "anti-leaky" (XIF)
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neurons (positive dissipation) as well as neurons with inverted sign of the leak current (negative dissipation) . We first show that such networkscan exhibit
neurons that generalize irregularly spiking non-chaotic LIF neuron networks. Endowed with simple conductance-based synapses for XIF neurons, our networks can generate
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, asynchronous spiking activity, if the neurons with negative dissipation are endowed with a voltage-dependent input cutoff, which may be interpreted as a simple conductance-based implementation of their synapses. We compute
asynchronous spiking as well. We determine
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for both types of neurons for
assuming Poisson input with
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assuming that inputs are Poissonian. The balanced state exists in a variety of neural network models and its dynamical properties such as chaoticity vary considerably. Our models generalize networks of leaky integrate-and-fire neurons where the dynamics are non-chaotic despite their irregularity. We show that switching the sign of the dissipation of a single neuron renders the entire network dynamics unstable and chaotic as indicated by a positive largest Lyapunov exponent. To further characterize the dynamics we consider
. Further, we compute
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and the related
(LEs) and the
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, which indicate the directions in which infinitesimal perturbations grow or shrink with a rate given by the Lyapunov exponents
specifying the corresponding perturbation directions
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for each ..
there is approximately one positive LE for each XIF neuron. This indicates in particular that a single XIF neuron renders the network dynamics chaotic. A simple mean-field approach, which can be justified by properties of the CLVs, explains the finding. As an application, we propose a spike-based computing scheme where our networks serve as computational reservoirs and their different stability properties yield different computational capabilities