Practical numerical algorithms for chaotic systems
Practical numerical algorithms for chaotic systems
Spiking Neuron Models: An Introduction
Spiking Neuron Models: An Introduction
SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Polychronization: Computation with Spikes
Neural Computation
Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems
Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems
Handbook of Networked and Embedded Control Systems (Control Engineering)
Handbook of Networked and Embedded Control Systems (Control Engineering)
Fundamental matrix solutions of piecewise smooth differential systems
Mathematics and Computers in Simulation
Simple model of spiking neurons
IEEE Transactions on Neural Networks
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Lyapunov exponents are a basic and powerful tool to characterise the long-term behaviour of dynamical systems. The computation of Lyapunov exponents for continuous time dynamical systems is straightforward whenever they are ruled by vector fields that are sufficiently smooth to admit a variational model. Hybrid neurons do not belong to this wide class of systems since they are intrinsically non-smooth owing to the impact and sometimes switching model used to describe the integrate-and-fire (I&F) mechanism. In this paper we show how a variational model can be defined also for this class of neurons by resorting to saltation matrices. This extension allows the computation of Lyapunov exponent spectrum of hybrid neurons and of networks made up of them through a standard numerical approach even in the case of neurons firing synchronously.