Self-Organization in a Parametrically Coupled Logistic Map Network: A Model for Information Processing in the Visual Cortex

Pashaie, Ramin; Farhat, Nabil H.

doi:10.1109/tnn.2008.2010703

Cited by 12 publications

(10 citation statements)

References 40 publications

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“…In other words, the cortical networks could be modeled with networks of parametrically coupled nonlinear iterative logistic maps each having complex dynamics that represents populations of randomly interconnected neurons possessing collective emergent properties (Pashaie and Farhat 2009). Moreover, symmetrically coupled logistic equations are proposed to mimic the competitive interaction between species (Lopez-Ruiz and Fournier-Prunaret 2009).…”

Section: Discussionmentioning

confidence: 99%

Synchrony based learning rule of Hopfield like chaotic neural networks with desirable structure

Mahdavi

Kurths

2013

Cogn Neurodyn

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In this paper a new learning rule for the coupling weights tuning of Hopfield like chaotic neural networks is developed in such a way that all neurons behave in a synchronous manner, while the desirable structure of the network is preserved during the learning process. The proposed learning rule is based on sufficient synchronization criteria, on the eigenvalues of the weight matrix belonging to the neural network and the idea of Structured Inverse Eigenvalue Problem. Our developed learning rule not only synchronizes all neuron's outputs with each other in a desirable topology, but also enables us to enhance the synchronizability of the networks by choosing the appropriate set of weight matrix eigenvalues. Specifically, this method is evaluated by performing simulations on the scale-free topology.

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Section: Discussionmentioning

confidence: 99%

Synchrony based learning rule of Hopfield like chaotic neural networks with desirable structure

Mahdavi

Kurths

2013

Cogn Neurodyn

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“…Despite having just one control parameter, this map could exhibit a variety of behavior, including the chaotic one. Its chaotic template has been spotted in the behavior of many biological systems, e.g., the heart and brain, together with their responses to various internal and external stimuli [35,47].…”

Section: Logistic Mapmentioning

confidence: 99%

Artificial neural network-based modeling of brain response to flicker light

et al. 2015

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Not only does the modeling of dynamical systems, for instance the biological systems, play an important role in the accurate perception and analysis of these systems, but it also makes the prediction and control of their behavior straightforward. The results of multiple researches in the field of the modeling of biological systems have indicated that the chaotic behavior is a prevalent feature of most complex interactive biological systems. Our results demonstrate that the artificial neural network provides us an effective means to model the underlying dynamics of these systems. In this paper, at first, we represent the results of the use of a multilayer feed-forward neural network to model some famous chaotic systems. The specified neural network is trained with the return maps extracted from the time series. We proceed with the paper by evaluating the accuracy and robustness of our model. The ability of the select neural network to model the dynamics of chosen chaotic systems is verified, even in the presence of noise. Afterwards, we model the brain response to the flicker light. It is known that the brain response to some stimuli such as the flicker light recorded as electroretinogram is an exemplar of chaotic behavior. The need remains, however, for realistic modeling of this behavior of the brain. In this paper, we represent the results of the modeling of this chaotic response by utilizing the proposed neural network. The capability of the neural network to model this specific brain response is confirmed.

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“…Its chaotic pattern has been spotted in the behavior of many biological systems, e.g. the heart and brain, together with their responses to various internal and external stimuli [5,9].…”

Section: Logistic Mapmentioning

confidence: 99%

Pragmatic modeling of chaotic dynamical systems through artificial neural network

Falahian

Dastjerdi

Gharibzadeh

2014

2014 21th Iranian Conference on Biomedical Engineering (ICBME)

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The precipitous advancements in the field of modeling of dynamical systems, which are the result of numerous relevant investigations, are the evidence of its fundamental importance. Not only does the modeling of the behavior of dynamical systems such as biological systems play an important role in the accurate perception and analysis of these systems, but it also becomes feasible to perfectly predict and control their behaviors. The results of the majority of these researches have indicated that chaotic behavior is a prevalent feature of complex interactive systems. Our achieved results indicate that artificial neural networks provide us the most efficacious means to model the underlying dynamics of these systems. In this paper, we represent the results of utilizing a specific neural network to model some famous chaotic systems such as Lorenz. The main aspect of our technique is training the neural network with a chaotic map. With this aim, at first, bifurcation diagram of the points obtained by applying Poincare section on the time series is plotted. The specified neural network is then trained with the extracted map. We conclude the paper by evaluating the accuracy and robustness of our model. The capability of the selected neural network to model the complex behavior of dynamical systems is indeed verified, even at the presence of noise.

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Self-Organization in a Parametrically Coupled Logistic Map Network: A Model for Information Processing in the Visual Cortex

Cited by 12 publications

References 40 publications

Synchrony based learning rule of Hopfield like chaotic neural networks with desirable structure

Synchrony based learning rule of Hopfield like chaotic neural networks with desirable structure

Artificial neural network-based modeling of brain response to flicker light

Pragmatic modeling of chaotic dynamical systems through artificial neural network

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