Neural Networks with Discontinuous/Impact Activations

This book presents as its main subject new models in mathematical neuroscience. A wide range of neural networks models with discontinuities are discussed, including impulsive differential equations, differential equations with piecewise constant arguments, and models of mixed type. These models involve discontinuities, which are natural because huge velocities and short distances are usually observed in devices modeling the networks. A discussion of the models, appropriate for the proposed applications, is also provided.

List of contents

Introduction.- Differential Equations with Piecewise Constant Argument of Generalized Type.- Impulsive Differential Equations.- Periodic Motions and Equilibria of Neural Networks with Piecewise Constant Argument.- Equilibria of Neural Networks with Impact Activation and Piecewise Constant Argument.- Periodic Motions of Neural Networks with Impact Activation and Piecewise Constant Argument.- The Method of Lyapunov Functions: RNNs.- The Lyapunov-Razumikhin Method: CNNs.

Summary

This book presents as its main subject new models in mathematical neuroscience. A wide range of neural networks models with discontinuities are discussed, including impulsive differential equations, differential equations with piecewise constant arguments, and models of mixed type. These models involve discontinuities, which are natural because huge velocities and short distances are usually observed in devices modeling the networks. A discussion of the models, appropriate for the proposed applications, is also provided.

Product details

• Authors: Mara Akhmet, Marat Akhmet, Enes Y lmaz, Enes Y. Lmaz, Enes Yilmaz, Enes Yılmaz
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2016
• EAN: 9781493945986
• ISBN: 978-1-4939-4598-6
• No. of pages: 168
• Dimensions: 155 mm x 10 mm x 235 mm
• Weight: 283 g
• Illustrations: XI, 168 p. 28 illus., 23 illus. in color.
• Series: Nonlinear Systems and Complexity; Nonlinear Systems and Complexity
• Subjects: Natural sciences, medicine, IT, technology > Technology > General, dictionaries; Social sciences, law, business > Media, communication > Book trade, library system; Analysis, B, Artificial Intelligence, engineering, complexity, Ordinary Differential Equations, Differential calculus & equations, Differential equations, Biomedical Engineering and Bioengineering, Biomedical engineering, Mathematical modelling, Neural networks (Computer science), Applied Dynamical Systems, Computational complexity