Chaotic Neuron Research Articles

Collective behaviors of neural network regulated by the spatially distributed stimuli

Most external stimuli, including sound, temperature, and illumination, exhibit spatially heterogeneous, and different amplitudes of the same signal are received by neurons at different positions in the neural network. To address this issue, we constructed a grid-like neural network using memristive FitzHugh-Nagumo neurons. The neuronal responses depend on the spatially distributed stimuli, with the stimulus amplitudes being determined by the distance from the central area. Consequently, complete synchronization occurs in the network comprising periodic neurons, chaotic neurons, and their hybrid forms. Periodic patterns maintain the highest Hamilton energy whereas the lowest Hamilton energy appears in chaotic neurons. In a network consisting of chaotic neurons, the synchronization threshold is larger compared to the other types. In particular, the periodic neurons with the highest energy oscillations can regulate the low-energy chaotic neurons into periodic patterns. Similar conclusions are drawn in a chain-like network. The results advance the understanding of the synchronization mechanisms in the presence of spatial heterogeneity.

A chaotic memristive Hindmarsh-Rose neuron with hybrid offset boosting

In recent years, memristor has been widely introduced into neuronal models to simulate magnetically induced currents. However, there are relatively few studies on electric field stimulation of neuronal models. This paper presents a 4D memristive Hindmarsh-Rose (HR) neuron model that introduces a sinusoidal function memristor and electric field variables, which can produce heterogeneous multistability and homogeneous multistability. More interestingly, six modes of offset boosting can be triggered in the neuronal model by varying the electric field coupling coefficients, the first three of which are parameter-dependent two-dimensional offset boosting modes, and the second three are initial-value-dependent offset-boosting modes. Notably, homogeneous multistability can also combined with the offset-boosting, and then iterating cubic infinitely many attractors. This model presents a model where multiple offset boosting is freely controllable for the first time. Finally, the theoretical analysis is verified by digital circuits on a RISC-V platform.

Energy balance and synchronization of the cross-ring photosensitive neural network

After detecting different external light stimuli, photosensitive neurons encode these stimuli and trigger different discharge patterns and membrane potentials, thereby transmitting signals in the neural network. The cross-ring structure can simulate complex dynamic behaviors in the neuron system, which helps to achieve synchronous behavior between neurons. This article, respectively, uses linear resistors and induction coils to connect four photosensitive neurons and constructs a cross-ring photosensitive neural network. We examine the energy balance and synchronization stability of the system by adjusting the coupling channels and external stimuli while also estimating the impact of noise. A system composed of identical neurons achieves energy balance and complete synchronization, whereas a system composed of diverse neurons is able to achieve phase synchronization by adjusting the coupling gain. However, under magnetic field coupling, a system composed of the same chaotic neurons can only achieve energy balance and complete synchronization with a larger coupling gain. For both types of coupled systems, noise may affect the synchronization of neuron systems in chaotic states, but it has no effect on the synchronization of spike-shaped neuron systems. Resistance coupling can synchronize more quickly than magnetic field coupling, but magnetic field coupling is more susceptible to variations in the coupling gain ratio. The study will give the domains of neuroscience and artificial intelligence a theoretical groundwork as well as a deeper knowledge of the workings and governing principles of neural networks.

Energy consumption in the synchronization of neurons coupled by electrical or memristive synapse

The energy consumption in synapses has been an issue of great concern, and we apply the resistor to function as the electrical synapse, and the memristor is utilized as the chemical synapse. We investigate the dynamics of neurons during the synchronization, as well as the energy consumption associated with coupled channels. The numerical results revealed that two neurons with different initial values can get into a complete synchronization, regardless of whether they are coupled via resistive or memristive synapse. Furthermore, the energy consumption of electrical synaptic coupling is companied by an energy phase transition burst that causes a sharp increase or decrease in the channel energy consumption. In contrast, memristive coupling promotes steady information and energy exchange between neurons, with relatively lower energy consumption compared to electrical synaptic coupling. Meanwhile, the memconductance of the memristor is lower than that of resistive coupling, leading to a lower coupling strength when the synchronization is achieved. Furthermore, the employment of the energy switch to trigger synaptic activation or silence can effectively control synaptic activity, and neurons can spontaneously synchronize and maintain energy balance. The energy difference between chaotic neurons can cause the transitions between synchronization, desynchronization, and resynchronization. The findings may provide insights for developing genuine neural circuits and leveraging them in artificial neuron design.

Cupolets: History, Theory, and Applications

In chaos control, one usually seeks to stabilize the unstable periodic orbits (UPOs) that densely inhabit the attractors of many chaotic dynamical systems. These orbits collectively play a significant role in determining the dynamics and properties of chaotic systems and are said to form the skeleton of the associated attractors. While UPOs are insightful tools for analysis, they are naturally unstable and, as such, are difficult to find and computationally expensive to stabilize. An alternative to using UPOs is to approximate them using cupolets. Cupolets, a name derived from chaotic, unstable, periodic, orbit-lets, are a relatively new class of waveforms that represent highly accurate approximations to the UPOs of chaotic systems, but which are generated via a particular control scheme that applies tiny perturbations along Poincaré sections. Originally discovered in an application of secure chaotic communications, cupolets have since gone on to play pivotal roles in a number of theoretical and practical applications. These developments include using cupolets as wavelets for image compression, targeting in dynamical systems, a chaotic analog to quantum entanglement, an abstract reducibility classification, a basis for audio and video compression, and, most recently, their detection in a chaotic neuron model. This review will detail the historical development of cupolets, how they are generated, and their successful integration into theoretical and computational science and will also identify some unanswered questions and future directions for this work.

A joint image encryption based on a memristive Rulkov neuron with controllable multistability and compressive sensing

Image encryption, as a critical branch, has attracted increasing attention to the demand for information security specifically in the era of artificial intelligence (AI). A chaotic sequence is regarded as an important encryption source, and compressive sensing provides an effective technology for obtaining and reconstructing sparse or compressible signals in applied electronic engineering. In this work, the detouring matching pursuit algorithm and DNA coding are utilized to increase the performance based on a newly developed chaotic firing neuron. A memristor as the electromagnetic component is proven to enhance synaptic plasticity and emulate the synaptic connections in the brain. A unique discrete memristive neuron is derived for exploring the dynamics of neuron firing. By modifying the feedback from the memristor various coexisting neuronal chaotic firing are possessed. Because of the periodic evolution of the resistor from the memristor, the derived memristive Rulkov neuron exhibits coexisting homogeneous and heterogeneous multistability, which enables amplitude controllability and different types of coexisting chaotic firings. Circuit implementation based on CH32 is built to verify the controllability of the coexisting dynamics.

Collective behaviors of fractional-order FithzHugh–Nagumo network

Brain connection is the mechanism of determining the brain function and cognition, and the small world network is widely investigated among these connections. In this paper, the small world complex brain network is constructed by the fractional-order neurons, and the fractional-order memristor is used to connect these neurons. Compared with the integer-order counterpart, the fractional-order memristor describes precisely the distortion of hysteresis curves, and it exhibits more abundant dynamical behaviors to function as the synapse. In addition, the neurons with different fractional orders represent the individual differences during the cell differentiation. For the two coupled neurons, the phase lock is achieved in the bursting and spiking neurons, and it denotes a time delay between the two firing process, whereas the chaotic neurons cannot synchronize. In small world network, the collective behaviors of neurons tend to synchronize with the increasing of the coupling intensity. These results promote the understanding of information coding and transformation in complex brain network.

Chaotic single neuron model with periodic coefficients with period two

Our goal is to investigate the piecewise linear difference equation xn+1 = βnxn – g(xn). This piecewise linear difference equation is a prototype of one neuron model with the internal decay rate β and the signal function g. The authors investigated this model with periodic internal decay rate βn as a period-two sequence. Our aim is to show that for certain values of coefficients βn, there exists an attracting interval for which the model is chaotic. On the other hand, if the initial value is chosen outside the mentioned attracting interval, then the solution of the difference equation either increases to positive infinity or decreases to negative infinity.

A Chaotic Neuron and its Ability to Prevent Overfitting

Chaotic neuron is a neural model based on chaos theory, which combines the complex dynamic behavior of biological neurons with the characteristics of chaotic systems. Inspired by the chaotic firing characteristics of biological neurons, a novel chaotic neuron model and its response activation function LMCU are proposed in this paper. Based on one-dimensional chaotic mapping, this chaotic neuron model takes the emissivity of chaotic firing characteristics of biological neurons as its response output, so that it has the nonlinear response and chaotic characteristics of biological neurons. Different from the traditional neuron model, it makes full use of the nonlinear dynamics of the chaotic system to achieve the activation output. In this paper, we apply the proposed chaotic neurons to artificial neural networks by using LeNet-5 models on MNIST and CIFAR-10 datasets, and compare them with common activation functions. The application of chaotic neurons can effectively reduce the overfitting phenomenon of artificial neural network, significantly reduce the generalization error of the model, and greatly improve the overall performance of artificial neural network. The innovative design of this chaotic neuron model provides a new cornerstone for the future development of artificial neural networks.

Predicting Cryptocurrency Fraud Using ChaosNet: The Ethereum Manifestation

Cryptocurrencies are in high demand now due to their volatile and untraceable nature. Bitcoin, Ethereum, and Dogecoin are just a few examples. This research seeks to identify deception and probable fraud in Ethereum transactional processes. We have developed this capability via ChaosNet, an Artificial Neural Network constructed using Generalized Luröth Series maps. Chaos has been objectively discovered in the brain at many spatiotemporal scales. Several synthetic neuronal simulations, including the Hindmarsh–Rose model, possess chaos, and individual brain neurons are known to display chaotic bursting phenomena. Although chaos is included in several Artificial Neural Networks (ANNs), for instance, in Recursively Generating Neural Networks, no ANNs exist for classical tasks entirely made up of chaoticity. ChaosNet uses the chaotic GLS neurons’ property of topological transitivity to perform classification problems on pools of data with cutting-edge performance, lowering the necessary training sample count. This synthetic neural network can perform categorization tasks by gathering a definite amount of training data. ChaosNet utilizes some of the best traits of networks composed of biological neurons, which derive from the strong chaotic activity of individual neurons, to solve complex classification tasks on par with or better than standard Artificial Neural Networks. It has been shown to require much fewer training samples. This ability of ChaosNet has been well exploited for the objective of our research. Further, in this article, ChaosNet has been integrated with several well-known ML algorithms to cater to the purposes of this study. The results obtained are better than the generic results.

Analysis on responses of chaotic Izhikevich neurons to periodic forcing

Analysis on responses of chaotic Izhikevich neurons to periodic forcing

Firing patterns and synchronization of Morris-Lecar neuron model with memristive autapse

Autapse is a self-feedback current in some neurons that can substantially affect the neuron’s characteristics. Due to the importance of electromagnetic induction in the dynamical functions of the neurons, the memristive autapses have been introduced. This paper presents the 3D Morris-Lecar neuron model with a memristive autapse. The dynamics of the memristive autaptic model are investigated by varying autapse parameters. It is revealed that the memristive autapse can change the period of the neuron’s firing or even change its dynamics between periodic and chaotic firings. The results represent that the chaotic regions are extended with the increase in the autapse time delay. Moreover, the memristive autapse leads to the emergence of multistability. The synchronization of coupled memristive autaptic neurons is also examined. It is found that the synchronization of chaotic neurons is enhanced by considering the memristive autapse. With increasing the autapse gain, the required coupling strength for synchronization decreases.

Cupolets in a chaotic neuron model.

This paper reports the first finding of cupolets in a chaotic Hindmarsh-Rose neural model. Cupolets (chaotic, unstable, periodic, orbit-lets) are unstable periodic orbits that have been stabilized through a particular control scheme by applying a binary control sequence. We demonstrate different neural dynamics (periodic or chaotic) of the Hindmarsh-Rose model through a bifurcation diagram where the external input current, I, is the bifurcation parameter. We select a region in the chaotic parameter space and provide the results of numerical simulations. In this chosen parameter space, a control scheme is applied when the trajectory intersects with either of the two control planes. The type of the control is determined by a bit in a binary control sequence. The control is either a small microcontrol (0) or a large macrocontrol (1) that adjusts the future dynamics of the trajectory by a perturbation determined by the coding function r ( x ). We report the discovery of many cupolets with corresponding control sequences and comment on the differences with previously reported cupolets in the double scroll system. We provide some examples of the generated cupolets and conclude by discussing potential implications for biological neurons.

A PID controller for synchronization between master-slave neurons in fractional-order of neocortical network model

Modeling of the biological neurons is a way to understand the architecture of neural networks of the brain. A complex brain network includes the synchronization between some groups of neurons. The dynamic behavior of interactions between groups of slave-master neurons in the neocortical network is unpredictable and challenging. The purpose of synchronizing a neural interaction is to reduce the synchronization error between the chaotic slave-master neurons. This paper uses a proportional–integral–derivative (PID) controller to synchronize master–slave neurons in the fractional-order of the neocortical network model based on dendritic spike frequency adaptation (DSFA) uncertainties and unknown disturbance effects. The purpose of this article is in two parts: First, we implemented the effect of previous states of the neuron conditions by fractional-order of the differential equations in the neocortical network model. Second, by synchronizing the FO neocortical master–slave model by PID controller, we investigated the connection strength of the complex network in chaotic point of view. The optimized PID coefficients and fractional-order were calculated using root mean square error (RMSE) criteria to control the membrane voltage synchronization. The chaotic behavior of the system was evaluated by numerical techniques such as attractor analysis and time series diagrams. The optimal RMSE value for master–slave neurons occurred at fractional-orders 0.89. It is shown that the synchronization of master–slave neurons improves over time, and eventually they are fully synchronized while the controller error is reduced.

Complex Dynamics of Noise-Perturbed Excitatory-Inhibitory Neural Networks With Intra-Correlative and Inter-Independent Connections.

Real neural system usually contains two types of neurons, i.e., excitatory neurons and inhibitory ones. Analytical and numerical interpretation of dynamics induced by different types of interactions among the neurons of two types is beneficial to understanding those physiological functions of the brain. Here, we articulate a model of noise-perturbed random neural networks containing both excitatory and inhibitory (E&I) populations. Particularly, both intra-correlatively and inter-independently connected neurons in two populations are taken into account, which is different from the most existing E&I models only considering the independently-connected neurons. By employing the typical mean-field theory, we obtain an equivalent system of two dimensions with an input of stationary Gaussian process. Investigating the stationary autocorrelation functions along the obtained system, we analytically find the parameters’ conditions under which the synchronized behaviors between the two populations are sufficiently emergent. Taking the maximal Lyapunov exponent as an index, we also find different critical values of the coupling strength coefficients for the chaotic excitatory neurons and for the chaotic inhibitory ones. Interestingly, we reveal that the noise is able to suppress chaotic dynamics of the random neural networks having neurons in two populations, while an appropriate amount of correlation coefficient in intra-coupling strengths can enhance chaos occurrence. Finally, we also detect a previously-reported phenomenon where the parameters region corresponds to neither linearly stable nor chaotic dynamics; however, the size of the region area crucially depends on the populations’ parameters.

Resonant neuronal groups

We create a Spiking Neural Network (SNN) architecture based on transforming the dynamics – Unstable Periodic Orbits (UPOs) – of a chaotic spiking neuron model to Neuronal Groups composed from Resonant Neurons. An input fed to the SNN will activate one of its neuronal groups. An activated neuronal group represents ‘memory’ or a neural state of the SNN. By exploiting a fundamental principle in chaos theory, which is Chaotic Sensitivity upon Initial Conditions, in conjunction with chaos control, we show that similar inputs, when fed separately to the SNN, will always activate the same neuronal group and different inputs will activate different neuronal groups. In addition, we show that differences between the system responses (i.e. neuronal groups) are proportional to differences between inputs. These features make the system suitable for input discrimination; we give an example of discerning human physical actions. More importantly, we study the capacity of the SNN. We show that the number of neuronal groups that can be reached is extremely large; it grows exponentially with the increase of the network size (i.e. number of neurons). This is due to neurons mixing, which allows the same resonant neuron to belong to other neuronal groups and due to the theoretically infinite number of UPOs available in a chaotic system that can be stabilized through chaos control. Also, our work competes with Izhikevich's polychronous groups, so we compare our results to his. We discuss the relevance of the work in the nonlinear sciences and its relation to chaotic neuro-dynamics, cognitive science, neural computation, machine learning and memory modeling including future considerations and open problems.

Dynamical System in Chaotic Neurons with Time Delay Self‐Feedback and Its Application in Color Image Encryption

The time delay caused by transmission in neurons is often ignored, but it is demonstrated by theories and practices that time delay is unavoidable. A new chaotic neuron model with time delay self‐feedback is proposed based on Chen’s chaotic neuron. The bifurcation diagram and Lyapunov exponential diagram are used to analyze the chaotic characteristics of neurons in the model when they receive the output signals at different times. The experimental results exhibit that it has a rich dynamic behavior. In addition, the randomness of chaotic series generated by chaotic neurons with time delay self‐feedback under different conditions is verified. In order to investigate the application of this model in image encryption, an image encryption scheme is proposed. The security analysis of the simulation results shows that the encryption algorithm has an excellent anti‐attack ability. Therefore, it is necessary and practical to study chaotic neurons with time delay self‐feedback.

Dynamics of Discrete Memristor-Based Rulkov Neuron

Continuous-time memristor have been widely used in fields such as chaotic circuits and neuromorphic computing systems, however, research on the application of discrete memristors haven’t been noticed yet. In this paper, a new chaotic neuron is firstly designed by applying the discrete memristor to two-dimensional Rulkov neuron. And then the dynamical behaviors of the discrete memristor-based neuron are analyzed by experiments including phase diagram, bifurcation, and spectral entropy complexity algorithm. The results show that the resistance of memristor has an important effect on the system dynamics, which delays the occurrence of bifurcation, in particular, the bifurcation disappears and the system reaches the fixed point of the neuron when the resistance is greater than a threshold. It is also found that with the increase of the current gain, the bursting activity becomes higher in frequency and wider range of high complexity is obtained. The results of our study show that the performance of Rulkov neuron is improved by applying the discrete memristor, and may provide new insights into the mechanism of memory and cognition in the nervous.

A Global Optimization Algorithm for Unconstrained Non-linear Optimization Problems Using Chaotic Neuron Map and Golden Number

This paper presents aninnovative global multi-variable optimization algorithm using one of the best chaotic sequences, the neuron map, a description of which is also provided in the paper. The algorithm uses neuron map in the first stage to move near the global minimum point, as well as in each iteration of the second stage of local search that is done using the N-dimensional golden section search algorithm. The generation and mapping of the neuron variables to the optimization variables along with the stagewise search for the global minimum is explained conscientiously in the work. Numerical results on some benchmark functions and the comparison with a latest state-of-the-art algorithm ispresented in order to demonstrate the efficiency of the proposed algorithm.

Kalman observers in estimating the states of chaotic neurons for image encryption under MQTT for IoT protocol

Kalman observers in estimating the states of chaotic neurons for image encryption under MQTT for IoT protocol