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Synchronisation of two different uncertain fractional-order chaotic systems with unknown parameters using a modified adaptive sliding-mode controller
This article investigates a modified adaptive sliding-mode controller to achieve synchronisation between two different fractional-order chaotic...
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Finite-Time and Fixed-Time Synchronization of Inertial Neural Networks with Mixed Delays
This paper considers the drive-response synchronization in finite-time and fixed-time of inertial neural networks with time-varying and distributed...
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Results on passivity analysis of delayed fractional-order neural networks subject to periodic impulses via refined integral inequalities
This manuscript is concerned with analysing the passiveness of fractional-order neural networks with parameter uncertainties, delays, and periodic...
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Noise-driven bifurcations in a neural field system modelling networks of grid cells
The activity generated by an ensemble of neurons is affected by various noise sources. It is a well-recognised challenge to understand the effects of...
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Neural field models with transmission delays and diffusion
A neural field models the large scale behaviour of large groups of neurons. We extend previous results for these models by including a diffusion term...
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Weakly coupled oscillator networks
The complexity and functionality of the human brain comes from the joint action of populations of cells acting in concert. The preceding chapters...
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Multistability Analysis and Adaptive Feedback Control on a New Financial Risk System
This study presents the findings of a new financial risk system with one absolute function and two quadratic nonlinearities. The rich dynamic...
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Dynamics behavior for second-order neutral Clifford differential equations: inertial neural networks with mixed delays
In this paper, Clifford-valued inertial neutral neural networks with time-varying delays and infinite distributed delay are investigated. With the...
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Stability of Coupled Systems of Stochastic Cohen-Grossberg Neural Networks with Time Delays, Impulses and Markovian Switching
This paper covers the topic of the pth moment (p ≥ 2) stability of coupled systems of stochastic Cohen-Grossberg neural networks with time delays,...
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Response properties of single neurons
Neurons are often viewed as biological filters that convert input signals to output signals. This perspective allows specific neural systems to be...
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Dynamics of unidirectionally-coupled ring neural network with discrete and distributed delays
In this paper, we consider a ring neural network with one-way distributed-delay coupling between the neurons and a discrete delayed self-feedback. In...
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A perspective on graph theory-based stability analysis of impulsive stochastic recurrent neural networks with time-varying delays
In this work, the exponential stability problem of impulsive recurrent neural networks is investigated; discrete time delay, continuously distributed...
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Firing rate tissue models
Despite the success of population models, such as the neural mass models described in Chap. 8 , in...
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Fast Voltage Dynamics of Voltage–Conductance Models for Neural Networks
We present the conductance limit of the voltage–conductance model with random firing voltage when conductance dynamics are slower than the voltage...
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Overview
The book is organised in chapters that progress from the scale of a single cell up to an entire brain. The use of mathematical methodologies does not...
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M-current induced Bogdanov–Takens bifurcation and switching of neuron excitability class
In this work, we consider a general conductance-based neuron model with the inclusion of the acetycholine sensitive, M-current. We study bifurcations...
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Population models
Ever since the first recordings of the humanElectroencephalogram electroencephalogram (EEG) in 1924 by Hans Berger [72], electrophysiological brain...
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Beginner’s guide to aggregation-diffusion equations
The aim of this survey is to serve as an introduction to the different techniques available in the broad field of aggregation-diffusion equations. We...
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Strongly coupled spiking networks
In Chap. 6 , we explored how collective behaviour, such as synchronous network oscillations and phase...
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Pinning Synchronization of Coupled Oscillators with Paired Topologies
This paper investigates the pinning synchronization of a group of coupled oscillators, where both the dissipative and restorative interactions are...