Chaotic Neuron Research Articles

What is the most suitable Lyapunov function?

• Algorithm for Hamilton energy function in dynamical system is clarified. • Hamilton energy function is the most suitable Lyapunov function for dynamical control. • Control of energy flow is the most effective way to synchronization control of chaotic systems. Lyapunov function provides feasible estimation and prediction of nonlinear system stability, and useful guidance for adaptive control in chaos and synchronization approach. In case of synchronization and control of chaotic systems, the involvement of adjustable gains in the Lyapunov function can be effective to optimize the convergence of orbits to stability and controllers within finite transient period. As a result, shorter transient period and lower power consumption can be approached by detecting the most suitable gains in the controllers and parameter observers. In this paper, we claim that the most suitable Lyapunov function can be the Hamilton energy for chaotic systems and more nonlinear dynamical systems, and so the parameter region for stability and controllability can be detected exactly, in addition, the reliability of controllers can be confirmed in practical way. Furthermore, the Lorenz and improved Chua oscillators in chaotic states are presented to confirm the dependence of Hamilton energy and stability on the intrinsic parameters and variables. It indicates that control of energy flow can be an effective scheme to control chaos in nonlinear systems and synchronization realization between chaotic systems, neurons and networks.

Energy-induced resonance synchronization in neural circuits

Biological neurons can be approached by using some functional neural circuits, and the biophysical mechanism for signal processing can be explained. Chemical stimulus can adjust the intracellular and extracellular ions concentration, and thus the channel current can be regulated to trigger appropriate firing modes in the neural activities. A physical stimulus often injects kinds of energy, and the energy can be encoded in the components for generating a certain channel current. The energy driving on the cell can be effective to enhance the pumping of ions and mode transition is induced. Based on a simple neural circuit exposed to the external magnetic field, the mode selection is investigated to explore the biophysical mechanism of energy absorption by applying periodic, and stochastic magnetic fields, respectively. The external field energy is encoded in the induction coil of the neural circuit, and the channel current is induced. Two identical neural circuits are exposed to the same magnetic field and the synchronization approach is investigated without synapse coupling. It is found that two neurons in periodic firings can be synchronized under the same periodic or noise-like magnetic field even applying different initials, while intermittent phase lock is induced between two chaotic neurons. Stochastic variation in the external magnetic field can induce noisy induced electromotive force (IEF) and the firing mode is regulated effectively. When both noisy IEF and periodic stimulus are applied, synchronization stability between periodic neurons with initials diversity is enhanced while synchronization approach between chaotic neurons becomes difficult. In addition, the Hamilton energy in each neuron can keep pace with another neuron when complete synchronization is stabilized within a finite transient period. These results provide new insights to know the energy encoding mechanism in neural circuits and neurons exposed to external magnetic field.

A STDP Rule that Favours Chaotic Spiking over Regular Spiking of Neurons

We compare the number of states of a Spiking Neural Network (SNN) composed from chaotic spiking neurons versus the number of states of a SNN composed from regular spiking neurons while both SNNs implementing a Spike Timing Dependent Plasticity (STDP) rule that we created. We find out that this STDP rule favors chaotic spiking since the number of states is larger in the chaotic SNN than the regular SNN. This chaotic favorability is not general; it is exclusive to this STDP rule only. This research falls under our long-term investigation of STDP and chaos theory.

Synchronization of chaotic artificial neurons and its application to secure image transmission under MQTT for IoT protocol

Artificial neurons are quite useful to generate chaotic behavior, and they can be implemented on embedded systems like Raspberry Pi that include WiFi network connectivity. In this manner, this paper shows the use of some artificial neurons to generate chaotic binary sequences whose randomness is enhanced by post-processing approaches and measured by performing statistical NIST SP 800-22 tests. The chaotic neurons are synchronized by different methods and each neuron is implemented on a Raspberry Pi, which allows connectivity to a machine-to-machine (M2M) broker. This wireless connectivity advantage is exploited herein to develop a lightweight cryptographic application under the message queueing telemetry transport (MQTT) for Internet of Things (IoT) protocol. The synchronized neurons have a topology in which one Raspberry Pi works as publisher and can send encrypted information to multiple subscribers. Due to the chaotic behavior of the neurons, the Raspberry Pi acting as subscriber can recover the encrypted information if and only if it has the right key, i.e., the correct random binary sequence generated by the publisher. To augment the security against attacks, the chaotic neurons have different initial conditions before M2M synchronization is accomplished, and the color image encryption under MQTT for IoT is evaluated by performing correlation, histogram, variance, entropy, and NPCR tests.

Lag synchronization of coupled time-delayed FitzHugh\u2013Nagumo neural networks via feedback control

Synchronization plays a significant role in information transfer and decision-making by neurons and brain neural networks. The development of control strategies for synchronizing a network of chaotic neurons with time delays, different direction-dependent coupling (unidirectional and bidirectional), and noise, particularly under external disturbances, is an essential and very challenging task. Researchers have extensively studied the synchronization mechanism of two coupled time-delayed neurons with bidirectional coupling and without incorporating the effect of noise, but not for time-delayed neural networks. To overcome these limitations, this study investigates the synchronization problem in a network of coupled FitzHugh–Nagumo (FHN) neurons by incorporating time delays, different direction-dependent coupling (unidirectional and bidirectional), noise, and ionic and external disturbances in the mathematical models. More specifically, this study investigates the synchronization of time-delayed unidirectional and bidirectional ring-structured FHN neuronal systems with and without external noise. Different gap junctions and delay parameters are used to incorporate time-delay dynamics in both neuronal networks. We also investigate the influence of the time delays between connected neurons on synchronization conditions. Further, to ensure the synchronization of the time-delayed FHN neuronal networks, different adaptive control laws are proposed for both unidirectional and bidirectional neuronal networks. In addition, necessary and sufficient conditions to achieve synchronization are provided by employing the Lyapunov stability theory. The results of numerical simulations conducted for different-sized multiple networks of time-delayed FHN neurons verify the effectiveness of the proposed adaptive control schemes.

Dynamic Analysis and FPGA Implementation of New Chaotic Neural Network and Optimization of Traveling Salesman Problem

A neural network is a model of the brain’s cognitive process, with a highly interconnected multiprocessor architecture. The neural network has incredible potential, in the view of these artificial neural networks inherently having good learning capabilities and the ability to learn different input features. Based on this, this paper proposes a new chaotic neuron model and a new chaotic neural network (CNN) model. It includes a linear matrix, a sine function, and a chaotic neural network composed of three chaotic neurons. One of the chaotic neurons is affected by the sine function. The network has rich chaotic dynamics and can produce multiscroll hidden chaotic attractors. This paper studied its dynamic behaviors, including bifurcation behavior, Lyapunov exponent, Poincaré surface of section, and basins of attraction. In the process of analyzing the bifurcation and the basins of attraction, it was found that the network demonstrated hidden bifurcation phenomena, and the relevant properties of the basins of attraction were obtained. Thereafter, a chaotic neural network was implemented by using FPGA, and the experiment proved that the theoretical analysis results and FPGA implementation were consistent with each other. Finally, an energy function was constructed to optimize the calculation based on the CNN in order to provide a new approach to solve the TSP problem.

Quasiperiodic-Chaotic Neural Networks and Short-Term Analog Memory

A model of quasiperiodic-chaotic neural networks is proposed on the basis of chaotic neural networks. A quasiperiodic-chaotic neuron exhibits quasiperiodic dynamics that an original chaotic neuron does not have. Quasiperiodic and chaotic solutions are exclusively isolated in the parameter space. The chaotic domain can be identified by the presence of a folding structure of an invariant closed curve. Using the property that the influence of perturbation is conserved in the quasiperiodic solution, we demonstrate short-term visual memory in which real numbers are acceptable for representing colors. The quasiperiodic solution is sensitive to dynamical noise when images are restored. However, the quasiperiodic synchronization among neurons can reduce the influence of noise. Short-term analog memory using quasiperiodicity is important in that it can directly store analog quantities. The quasiperiodic-chaotic neural networks are shown to work as large-scale analog storage arrays. This type of analog memory has potential applications to analog computation such as deep learning.

Correlation Analysis of Synchronization Type and Degree in Respiratory Neural Network.

Pre-Bötzinger complex (PBC) is a necessary condition for the generation of respiratory rhythm. Due to the existence of synaptic gaps, delay plays a key role in the synchronous operation of coupled neurons. In this study, the relationship between synchronization and correlation degree is established for the first time by using ISI bifurcation and correlation coefficient, and the relationship between synchronization and correlation degree is discussed under the conditions of no delay, symmetric delay, and asymmetric delay. The results show that the phase synchronization of two coupling PBCs is closely related to the weak correlation, that is, the weak phase synchronization may occur under the condition of incomplete synchronization. Moreover, the time delay and coupling strength are controlled in the modified PBC network model, which not only reveals the law of PBC firing transition but also reveals the complex synchronization behavior in the coupled chaotic neurons. Especially, when the two coupled neurons are nonidentical, the complete synchronization will disappear. These results fully reveal the dynamic behavior of the PBC neural system, which is helpful to explore the signal transmission and coding of PBC neurons and provide theoretical value for further understanding respiratory rhythm.

A Novel Memristive Chaotic Neuron Circuit and Its Application in Chaotic Neural Networks for Associative Memory

In this article, we propose a novel chaotic neuron circuit with memristive neural synapses, construct an architecture of memristive chaotic neural network (MCNN) and implement associative memory application of bipolar images. The proposed neuron circuit mainly consists of synapse module and neuron module with chaotic dynamics characteristics. The synapse module is composed of memristors which represent synaptic weights. The neuron module employs voltage feedback operational amplifiers to accomplish integral operation and output function. MCNN utilizes a memristor crossbar array to perform matrix operations and can process the information in parallel. In addition, the proposed circuit of MCNN can accomplish continuous recursive operations and meet different applications due to the programmability of the memristor. The ex-situ method is utilized to train the memristor crossbar array. Furthermore, the associative memory applications of bipolar images are carried out based on the constructed circuits of MCNN with three and nine neurons. The simulation results in PSPICE software testify the functions of the MCNN circuit.

Sigmoidal synaptic learning produces mutual stabilization in chaotic FitzHugh–Nagumo model

This paper investigates the interaction between two coupled neurons at the terminal end of a long chain of neurons. Specifically, we examine a bidirectional, two-cell FitzHugh-Nagumo neural model capable of exhibiting chaotic dynamics. Analysis of this model shows how mutual stabilization of the chaotic dynamics can occur through sigmoidal synaptic learning. Initially, this paper begins with a bifurcation analysis of an adapted version of a previously studied FitzHugh-Nagumo model that indicates regions of periodic and chaotic behaviors. Through allowing the synaptic properties to change dynamically via neural learning, it is shown how the system can evolve from chaotic to stable periodic behavior. The driving factor between this transition is representative of a stimulus coming down a long neural pathway. The result that two chaotic neurons can mutually stabilize via a synaptic learning implies that this may be a mechanism whereby neurons can transition from a disordered, chaotic state to a stable, ordered periodic state that persists. This approach shows that even at the simplest level of two terminal neurons, chaotic behavior can become stable, sustained periodic behavior. This is achieved without the need for a large network of neurons.

ChaosNet: A chaos based artificial neural network architecture for classification.

Inspired by chaotic firing of neurons in the brain, we propose ChaosNet-a novel chaos based artificial neural network architecture for classification tasks. ChaosNet is built using layers of neurons, each of which is a 1D chaotic map known as the Generalized Luröth Series (GLS) that has been shown in earlier works to possess very useful properties for compression, cryptography, and for computing XOR and other logical operations. In this work, we design a novel learning algorithm on ChaosNet that exploits the topological transitivity property of the chaotic GLS neurons. The proposed learning algorithm gives consistently good performance accuracy in a number of classification tasks on well known publicly available datasets with very limited training samples. Even with as low as seven (or fewer) training samples/class (which accounts for less than 0.05% of the total available data), ChaosNet yields performance accuracies in the range of 73.89%-98.33%. We demonstrate the robustness of ChaosNet to additive parameter noise and also provide an example implementation of a two layer ChaosNet for enhancing classification accuracy. We envisage the development of several other novel learning algorithms on ChaosNet in the near future.

Necessary Conditions for Complete Synchronization of a Coupled Chaotic Aihara Neuron Network with Electrical Synapses

In this paper, the synchronization problem of a chaotic Aihara neuron network is considered. Based on the master stability function (MSF) analysis, some necessary conditions are proposed to investigate the complete synchronization of the electrical coupled chaotic Aihara neuron networks. Especially, the two-dimensional parameter-space plots are obtained numerically to visualize the possible synchronized region. For the chaotic Rulkov neuron network, the numerical simulations of the MSF show that complete synchronization of the electrical coupled Aihara neuron network can be achieved when the coupling strength lies in a suitable interval, while it is highly improbable to attain complete synchronization when all neurons are in the chaotic bursting. Moreover, the complete synchronization cannot be reached with further increase or decrease of coupling strength. These results are probably common features as far as discrete-time neuron networks are concerned. Finally, based on the drive-response active control method, an LMI-based criterion is obtained to ensure complete synchronization of the available chaotic Aihara neuron network. The spatiotemporal patterns measured by the state distribution of neurons are employed to validate the effectiveness of our control scheme.

Fourier analysis of a delayed Rulkov neuron network

We have analyzed the synchronization of some different networks of chaotic Rulkov neurons with an electrical coupling that contains a delay. We have developed an algorithm to compute a certain delay whose result is to improve the synchronization of the network when it was slightly synchronized, or to get synchronized when it was desynchronized. Our general approach has been to use tools from signal analysis, such as Fourier and wavelet transforms. With these tools, we have characterized the behavior of the neurons for different parameters in frequency and time-frequency domains. The algorithm has been applied for two well-known network models: the small-world and Erdös-Rényi. We have also tested the algorithm by using non-homogeneous neurons affected with a parametric noise.

Feedforward Chaotic Neural Network Model for Rotor Rub-Impact Fault Recognition Using Acoustic Emission Method

The rubbing faults caused by dynamic and static components in large rotatory machine are dangerous in manufacture process. This paper applies a feedforward chaotic neural network (FCNN) to recognize acoustic emission (AE) source in rotor rubbing and diagnose the rotor operational condition. This method adds the dynamic chaotic neurons based on logistic mapping into the multilayer perceptron (MLP) model to avoid the network falling into a local minimum, the delayed and feedback structure for maximum efficiency of recognition performance. The AE data was rotor rubbing process sampled from the test rig of rotatory machine, classification by fault degree. The experimental results indicate that the recognition rate is superior to the traditional BP network models. It is an effective method to recognize the rubbing faults for the machine normal operation.

Selective synchronization of coupled bifurcating neurons for phase shift of background oscillation

Synchronization in coupled bifurcating neurons was studied from the view point of the selective formation of cell assembly. The bifurcating neuron is a simple chaotic neuron that exhibits chaotic inter-spike interval dynamics via the addition of sinusoidal background oscillation. In this research, we introduced the phase shift of the background oscillation and several types of phase response to the input spike sequence. Sixteen coupled bifurcating neurons with complete bidirectional coupling were numerically simulated and their synchronized behaviors were analyzed. As a result, the formation of chaotically synchronized cell assemblies for the phase shift value were observed.

Recurrence quantification analysis for the identification of burst phase synchronisation.

In this work, we apply the spatial recurrence quantification analysis (RQA) to identify chaotic burst phase synchronisation in networks. We consider one neural network with small-world topology and another one composed of small-world subnetworks. The neuron dynamics is described by the Rulkov map, which is a two-dimensional map that has been used to model chaotic bursting neurons. We show that with the use of spatial RQA, it is possible to identify groups of synchronised neurons and determine their size. For the single network, we obtain an analytical expression for the spatial recurrence rate using a Gaussian approximation. In clustered networks, the spatial RQA allows the identification of phase synchronisation among neurons within and between the subnetworks. Our results imply that RQA can serve as a useful tool for studying phase synchronisation even in networks of networks.

A Study on Output Voltage of a Chaotic Neuron Model with Low Capacity

A Study on Output Voltage of a Chaotic Neuron Model with Low Capacity

Different characteristics and important channels between the healthy brain network and the epileptic brain network based on EEG data

In this paper, firstly, based on the clinic EEG data taken from 19 channels (electrodes, nodes) on human scalp, assuming that each electrode can be represented by a two-dimensional Rulkov chaotic neuron model, and the connectivity between any two electrodes may be the non-directional coupling, the healthy brain network and the epileptic brain network are established. Secondly, different dynamical characteristics between the two networks are investigated by the master stability function analysis (MSF). The research shows that the two networks are unlikely to achieve stable synchronization when the coupling is linear and α ≥ 2.8. When the coupling is nonlinear, there exist some α such that the epileptic brain network can achieve stable synchronization for ε ∈ [0.1678, 0.1694], while the healthy brain network is unlikely to achieve stable synchronization. Finally, based on graph theory and index of node importance, several kinds of evaluation indexes of node are calculated, such as degree, average path length and clustering coefficient. This investigation shows that the average degree and the average clustering coefficient of the epileptic brain network are larger than those of the healthy network. However, the average path length of the epileptic brain network is smaller than that of the healthy network. For other indexes, compared with the corresponding indexes of the healthy brain network, subgraph centricity, eigenvector, closeness and cumulated nomination of the epileptic brain network are increased or decreased, simultaneously. Channels Fp1, T5, Pz and Fp2 can be regarded as important focal zones for the occurrence of epilepsy.

Spatiotemporal activities of a pulse-coupled biological neural network

The present work is on the spatiotemporal activities and effects of chaotic neurons in a pulse-coupled biological neural network. The biological neural network used is that of Caenorhabditis elegans. Because of its similarity to human neural network, it can be used to understand the simple dynamics of human brain. Within the network the neurons are found to exhibit chaotic nature, even though their parameters are that of normal neurons. It is observed that when the strength of synaptic conductance is increased, initially the bursting synchronization, entropy of the network and the average firing rate decrease slightly and then increase. Since chaotic dynamics of neuron plays an important role in human brain functions, the neurons of the network are intentionally made chaotic and the dynamics is studied. As the neurons of the network are made chaotic, ‘near-death’-like surges of neuron activity before ending firing is observed throughout the network. Also, the brain dynamics changes from alert to rest state. When most of the neurons of the network are made chaotic, their activities become independent of the coupling strength.

Synchronization and chaos in coupled memristor-based FitzHugh-Nagumo circuits with memristor synapse

The memristor has drawn a significant interest in the fields of neuromorphic circuits because the nanoscale memristor is a strong candidate to become the critical element of novel ultra-high density low-power non-volatile memories. In the present paper, we focus on networks of FitzHugh-Nagumo neuron circuits employing memristor. First, we build the memristor-based circuit of FitzHugh-Nagumo model. The details of the chaotic phenomena of the memristor-based FitzHugh-Nagumo circuit under external stimuli have been found with use of computer simulations, i.e., we have numerically calculated waveformdiagrams, phase portraits, Lyapunov exponents and bifurcation diagram. And we also confirm these results of theoretical analyses and numerical calculations by circuit simulation experiments of the actual analog circuit realization using Multisim modeling. Then the synchronization of coupled memristor-based chaotic neurons with memristor synapse is discussed, and synchronization mechanism is also found. Finally, we have also derived the sufficient conditions of chaotic synchronization in unidirectional coupled neuron circuits and bidirectional coupled neuron circuits respectively, which are that the parameter of memristor synapse must meet certain conditions. These results of theoretical analyses have been confirmed by numerical simulation.