Convergent activation dynamics in continuous time networks
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IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
Robust Stability Criterion for Delayed Neural Networks with Discontinuous Activation Functions
Neural Processing Letters
ISNN '09 Proceedings of the 6th International Symposium on Neural Networks on Advances in Neural Networks
IEEE Transactions on Neural Networks
Universal analysis method for stability of recurrent neural networks with different multiple delays
ISNN'11 Proceedings of the 8th international conference on Advances in neural networks - Volume Part I
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Quasi-synchronization of delayed coupled networks with non-identical discontinuous nodes
ISNN'12 Proceedings of the 9th international conference on Advances in Neural Networks - Volume Part I
Information Sciences: an International Journal
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We use the concept of the Filippov solution to study the dynamics of a class of delayed dynamical systems with discontinuous right-hand side, which contains the widely studied delayed neural network models with almost periodic self-inhibitions, interconnection weights, and external inputs. We prove that diagonal-dominant conditions can guarantee the existence and uniqueness of an almost periodic solution, as well as its global exponential stability. As special cases, we derive a series of results on the dynamics of delayed dynamical systems with discontinuous activations and periodic coefficients or constant coefficients, respectively. From the proof of the existence and uniqueness of the solution, we prove that the solution of a delayed dynamical system with high-slope activations approximates to the Filippov solution of the dynamical system with discontinuous activations.