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Nonlinear Dynamics

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Constructing general partial differential equations using polynomial and neural networks.

Neural networks : the official journal of the International Neural Network Society
Sum fraction terms can approximate multi-variable functions on the basis of discrete observations, replacing a partial differential equation definition with polynomial elementary data relation descriptions. Artificial neural networks commonly transfo...

Distributed parameter estimation in unreliable sensor networks via broadcast gossip algorithms.

Neural networks : the official journal of the International Neural Network Society
In this paper, we present an asynchronous algorithm to estimate the unknown parameter under an unreliable network which allows new sensors to join and old sensors to leave, and can tolerate link failures. Each sensor has access to partially informati...

Neural networks for tracking of unknown SISO discrete-time nonlinear dynamic systems.

ISA transactions
This article presents a Lyapunov function based neural network tracking (LNT) strategy for single-input, single-output (SISO) discrete-time nonlinear dynamic systems. The proposed LNT architecture is composed of two feedforward neural networks operat...

A Unified Framework for Reservoir Computing and Extreme Learning Machines based on a Single Time-delayed Neuron.

Scientific reports
In this paper we present a unified framework for extreme learning machines and reservoir computing (echo state networks), which can be physically implemented using a single nonlinear neuron subject to delayed feedback. The reservoir is built within t...

Structure Identification of Uncertain Complex Networks Based on Anticipatory Projective Synchronization.

PloS one
This paper investigates a method to identify uncertain system parameters and unknown topological structure in general complex networks with or without time delay. A complex network, which has uncertain topology and unknown parameters, is designed as ...

Basin stability for burst synchronization in small-world networks of chaotic slow-fast oscillators.

Physical review. E, Statistical, nonlinear, and soft matter physics
The impact of connectivity and individual dynamics on the basin stability of the burst synchronization regime in small-world networks consisting of chaotic slow-fast oscillators is studied. It is shown that there are rewiring probabilities correspond...

Genetic programming based quantitative structure-retention relationships for the prediction of Kovats retention indices.

Journal of chromatography. A
The development of quantitative structure-retention relationships (QSRR) aims at constructing an appropriate linear/nonlinear model for the prediction of the retention behavior (such as Kovats retention index) of a solute on a chromatographic column....

Nonsmooth Finite-Time Synchronization of Switched Coupled Neural Networks.

IEEE transactions on cybernetics
This paper is concerned with the finite-time synchronization (FTS) issue of switched coupled neural networks with discontinuous or continuous activations. Based on the framework of nonsmooth analysis, some discontinuous or continuous controllers are ...

Impact of sub and supra-threshold adaptation currents in networks of spiking neurons.

Journal of computational neuroscience
Neuronal adaptation is the intrinsic capacity of the brain to change, by various mechanisms, its dynamical responses as a function of the context. Such a phenomena, widely observed in vivo and in vitro, is known to be crucial in homeostatic regulatio...

Synchronization of a Class of Switched Neural Networks with Time-Varying Delays via Nonlinear Feedback Control.

IEEE transactions on cybernetics
This paper is concerned with the synchronization problem for a class of switched neural networks (SNNs) with time-varying delays. First, a new crucial lemma which includes and extends the classical exponential stability theorem is constructed. Then b...