Hindmarsh-Rose Model Research Articles

A Novel Approach to Generate Dynamic S-Box for Lightweight Cryptography Based on the 3D Hindmarsh Rose Model

A Novel Approach to Generate Dynamic S-Box for Lightweight Cryptography Based on the 3D Hindmarsh Rose Model

Markovian noise-induced delta synchronization approach for Hindmarsh–Rose model

The paper explores noise-induced synchronization in uncoupled Hindmarsh–Rose neurons, introducing two distinctive elements: the application of Markovian noise and an analysis of synchronization via unpredictability. The noise is defined as an unpredictable and continuous process with characteristics proper for stochasticity. While identical synchronization is also investigated, the primary focus is to reveal synchronization in noise intensity domains that elude conventional detection methods, through delta synchronization within the neural system. Furthermore, a stronger form of synchronization, namely complete synchronization of unpredictability, is found to emerge in the domain with identical synchronization. The research findings are substantiated by numerical outcomes assessing unpredictability and synchronization, alongside comprehensive tables displaying characteristic time sequences for synchronization.

Securing Parallel Data: An Experimental Study of Hindmarsh-Rose Model-Based Confidentiality

This paper presents a novel parallel computing confidentiality scheme based on the Hindmarsh-Rose model; a mathematical model commonly used to describe neuronal activity. In an era where data security is paramount, especially in parallel computing environments, this scheme offers a promising solution to enhance data privacy. We explore the Hindmarsh-Rose model's unique chaotic behavior to develop an encryption and decryption framework tailored to parallel computing. Empirical results demonstrate the scheme's efficiency and effectiveness in maintaining data confidentiality while ensuring timely access. The scalability and resource utilization aspects of the scheme are also discussed. This research contributes to the ongoing efforts to bolster data security in parallel computing and opens up new possibilities for utilizing mathematical models in cryptography

Coupling Relationships between the Brain and the Central Pattern Generator Based on a Fractional-Order Extended Hindmarsh-Rose Model.

The states of the central nervous system (CNS) can be classified into subcritical, critical, and supercritical states that endow the system with information capacity, transmission capabilities, and dynamic range. A further investigation of the relationship between the CNS and the central pattern generators (CPG) is warranted to provide insight into the mechanisms that govern the locomotion system. In this study, we established a fractional-order CPG model based on an extended Hindmarsh-Rose model with time delay. A CNS model was further established using a recurrent excitation-inhibition neuronal network. Coupling between these CNS and CPG models was then explored, demonstrating a potential means by which oscillations generated by a neural network respond to periodic stimuli. These simulations yielded two key sets of findings. First, frequency sliding was observed when the CPG was sent to the CNS in the subcritical, critical, and supercritical states with different external stimulus and fractional-order index values, indicating that frequency sliding regulates brain function on multiple spatiotemporal scales when the CPG and CNS are coupled together. The main frequency range for these simulations was observed in the gamma band. Second, with increasing external inputs the coherence index for the CNS decreases, demonstrating that strong external inputs introduce neuronal stochasticity. Neural network synchronization is then reduced, triggering irregular neuronal firing. Together these results provide novel insight into the potential mechanisms that may underlie the locomotion system.

Hamiltonian energy in a modified Hindmarsh-Rose model.

This paper investigates the Hamiltonian energy of a modified Hindmarsh-Rose (HR) model to observe its effect on short-term memory. A Hamiltonian energy function and its variable function are given in the reduced system with a single node according to Helmholtz's theorem. We consider the role of the coupling strength and the links between neurons in the pattern formation to show that the coupling and cooperative neurons are necessary for generating the fire or a clear short-term memory when all the neurons are in sync. Then, we consider the effect of the degree and external stimulus from other neurons on the emergence and disappearance of short-term memory, which illustrates that generating short-term memory requires much energy, and the coupling strength could further reduce energy consumption. Finally, the dynamical mechanisms of the generation of short-term memory are concluded.

Chimera states in a lattice of superdiffusively coupled neurons

Chimera states are a truly remarkable dynamical phenomenon that occur in systems of coupled oscillators. In this regime, regions of synchronized and unsynchronized elements are formed in the system. For many applied problems, especially in neuroscience, these states offer a rich potential for research. However, the plethora of models and the lack of a ”single simple principle” that leads to the development of chimeras makes it very difficult to understand their nature. In this work, we propose a three-component reaction-superdiffusion system based on a unified mechanism founded on the properties of the fractional Laplace operator and the nonlinear Hindmarsh-Rose model functions. In the proposed system, the non-local type of interaction forming the coupling between the elements depends significantly on the fractional Laplace operator exponents of the corresponding components. It is shown that in the framework of the superdiffusion type of interaction, chimera states are realized in the system. At the same time, many qualitative (shape, visual degree of inhomogeneity and area size) and quantitative characteristics of chimeras (synchronization factor, strength of incoherence, local order parameter, number of elements with a potential value exceeding a given one) depend significantly on the exponents of the fractional Laplace operator. In addition to classical chimeras and target-waves chimeras, the results of numerical simulations show the presence of mutually sustaining reaction processes of different scales in the system.

Stochastic resonance in Hindmarsh-Rose neural model driven by multiplicative and additive Gaussian noise

This paper investigates the occurrence of stochastic resonance in the three-dimensional Hindmarsh-Rose (HR) neural model driven by both multiplicative and additive Gaussian noise. Firstly, the three-dimensional HR neural model is transformed into the one-dimensional Langevin equation of the HR neural model using the adiabatic elimination method, and the effects of HR neural model parameters on the potential function are analyzed. Secondly the Steady-state Probability Density (SPD), the Mean First-Passage Time (MFPT), and the Signal-to-Noise Ratio (SNR) of the HR neural model are derived, based on two-state theory. Then, the effects of different parameters (a, b, c, s), noise intensity, and the signal amplitude on these metrics are analyzed through theoretical simulations, and the behavior of particles in a potential well is used to analyze how to choose the right parameters to achieve high-performance stochastic resonance. Finally, numerical simulations conducted with the fourth-order Runge–Kutta algorithm demonstrate the superiority of the HR neural model over the classical bistable stochastic resonance (CBSR) in terms of performance. The peak SNR of the HR neural model is 0.63 dB higher than that of the CBSR system. Simulation results indicate that the occurrence of stochastic resonance occur happens in HR neural model under different values of parameters. Furthermore, under certain conditions, there is a ‘suppress’ phenomenon that can be produced by changes in noise, which provides great feasibilities and practical value for engineering application.

A new rolling bearing fault diagnoses method based on period-doubling bifurcation in the Hindmarsh–Rose model

The Hindmarsh–Rose (HR) model is a three-dimensional oscillators susceptible to initial values, making it capable of amplifying even the slightest variations. On this basis, we proposed a rolling bearing fault identification method based on period-doubling bifurcation in the HR model and constructed a bearing fault experimental platform to validate our approach in this paper. Initially, we analyze the HR model’s bifurcation characteristics using the discrete mapping method to identify oscillators suitable for detecting bearing faults. We then select the multiplicative period bifurcation points of the HR model to differentiate between different types of bearing faults. Next, we decompose and reconstruct vibration signals using the Hilbert–Huang transform and calculate the amplitude characteristics of the fault frequency band as the input for the HR detection oscillator. Finally, bearing faults are identified based on the phase trajectory of period-doubling. Furthermore, a comparative analysis is conducted between the proposed methodology and the employment of the empirical wavelet transform. Our approach presents a new perspective for utilizing nonlinear oscillators in bearing fault diagnosis.

Effect of cognitive training on brain dynamics

The human brain is highly plastic. Cognitive training is usually used to modify functional connectivity of brain networks. Moreover, the structures of brain networks may determine its dynamic behavior which is related to human cognitive abilities. To study the effect of functional connectivity on the brain dynamics, the dynamic model based on functional connections of the brain and the Hindmarsh–Rose model is utilized in this work. The resting-state fMRI data from the experimental group undergoing abacus-based mental calculation (AMC) training and from the control group are used to construct the functional brain networks. The dynamic behavior of brain at the resting and task states for the AMC group and the control group are simulated with the above-mentioned dynamic model. In the resting state, there are the differences of brain activation between the AMC group and the control group, and more brain regions are inspired in the AMC group. A stimulus with sinusoidal signals to brain networks is introduced to simulate the brain dynamics in the task states. The dynamic characteristics are extracted by the excitation rates, the response intensities and the state distributions. The change in the functional connectivity of brain networks with the AMC training would in turn improve the brain response to external stimulus, and make the brain more efficient in processing tasks.

Desynchronization of neuronal firing in multiparameter ultrasound stimulation

Low-intensity transcranial ultrasound stimulation, a novel neuromodulation technique, that possesses the advantages of non-invasiveness, high penetration depth, and high spatial resolution, has achieved positive neuromodulation effects in animal studies. But the regulatory mechanism remains controversial. The intramembrane cavitation effect is considered one of the mechanisms for ultrasound neuromodulation. In this study, the modified equations of ultrasonic cavitation bubble dynamics were coupled with the dual-coupled neuron Hindmarsh-Rose model, small-world neural network model, and the Jansen-Rit neural mass model, which simulate simple coupled neurons, complex neuronal networks, and discharge signals in epileptic disorders respectively. The results demonstrated that ultrasound stimulation has an appreciable modulatory effect on neuronal firing desynchronization in Hindmarsh-Rose model and small-world neural network model. The desynchronization effect is related to the stimulation frequency and intensity. Furthermore, ultrasound stimulation has an inhibitory effect on epileptic seizures, and the effect is enhanced by increasing ultrasound frequency from 0.1–1.0 MHz. This is the first combination of ultrasonic intramembrane cavitation effect theory with neurons and neural network firing desynchronization, which can provide guidance of parametric and theories support for the studies of neurological diseases such as epilepsy and Parkinson’s disease.

Influence of external current and noise on modes of electrical activities and energy of Hindmarsh-Rose model coupled by memristive synapses

The progress of medicine and biological have lengthen life, thus increasing the incidence of degenerative illnesses such as Parkinson, Alzheimer. To help patients suffering from those illnesses, we can use a therapy technique which consists to deliver within a precise region of the central nervous system an electrical signal in order to regulate unnatural impulses. That therapeutic method, since it requires surgical procedure is only needed when medication stops to have effect on the patients. In this work, we study the effects of periodic external current and noise on the modes of electrical activities; Furthermore we estimate the energy of a 2D Hindmarsh-Rose coupled by memristive synapses. Results show that the neuronal network exhibits bursting regime in the presence of periodic external force and noise. Noises make those bursts irregular over time evolution. Concerning the energy analysis, we observe an increase of the energy when the amplitude of the external force increases. Lastly, we show that noise makes the energy of the neuronal network to oscillate with different amplitudes. Large amplitude is observed in the presence of large values of the amplitude of the noise.

Cardiac behaviors and chaotic arrhythmias in the Hindmarsh–Rose model

The Hindmarsh–Rose is one of the best-known models of computational neuroscience. Despite its popularity as a neuron model, we demonstrate that it is also a complete cardiac model. We employ a method based on bifurcations of the interspike interval to redraw its phase diagram and reveal a cardiac region. This diagram bears great resemblance to that of the map-based model for neurons and cardiac cells, the KTz model. Both phase diagrams are compared, showing a very similar placement of behaviors in the parameter space. Adjusting the Hindmarsh–Rose parameters allows us to obtain behaviors similar to atrial, ventricular and pacemaker cells. We also report the neuronal behavior of sustained subthreshold oscillations in the diagram, also unknown in the model. We demonstrate the existence of periodic and chaotic early afterdepolarizations, a behavior linked to life-threatening arrhythmias. In a second phase diagram, we find a chaotic region with early afterdepolarizations and self-organized periodic structures known as shrimps. We also propose a new and simple method to calculate the electrocardiogram using the membrane potential of a point cell and demonstrate its use for the study of QT syndromes using the Hindmarsh–Rose model. Given the smaller number of equations and parameters than detailed conductance models and richer dynamics than other general models, this work presents the Hindmarsh–Rose as a promising alternative for computational cardiology studies.

A Bio-Inspired Chaos Sensor Model Based on the Perceptron Neural Network: Machine Learning Concept and Application for Computational Neuro-Science.

The study presents a bio-inspired chaos sensor model based on the perceptron neural network for the estimation of entropy of spike train in neurodynamic systems. After training, the sensor on perceptron, having 50 neurons in the hidden layer and 1 neuron at the output, approximates the fuzzy entropy of a short time series with high accuracy, with a determination coefficient of R2~0.9. The Hindmarsh-Rose spike model was used to generate time series of spike intervals, and datasets for training and testing the perceptron. The selection of the hyperparameters of the perceptron model and the estimation of the sensor accuracy were performed using the K-block cross-validation method. Even for a hidden layer with one neuron, the model approximates the fuzzy entropy with good results and the metric R2~0.5 ÷ 0.8. In a simplified model with one neuron and equal weights in the first layer, the principle of approximation is based on the linear transformation of the average value of the time series into the entropy value. An example of using the chaos sensor on spike train of action potential recordings from the L5 dorsal rootlet of rat is provided. The bio-inspired chaos sensor model based on an ensemble of neurons is able to dynamically track the chaotic behavior of a spike signal and transmit this information to other parts of the neurodynamic model for further processing. The study will be useful for specialists in the field of computational neuroscience, and also to create humanoid and animal robots, and bio-robots with limited resources.

A memristor-based circuit approximation of the Hindmarsh–Rose model

Neuron models exist in different levels of complexity and biological modeling depth. The Hindmarsh–Rose model offers a rich repertoire of neuronal dynamics while being moderately mathematically complex. Existing circuit realizations of this neuron model, however, require a large amount of operational amplifiers due to the model’s quadratic and cubic nonlinearity. In contrast to hardware realizations of simpler neuron models, this leads to a higher power consumption. In this work, the Hindmarsh–Rose model is approximated by an ideal electrical circuit that relies mostly on passive circuit elements and thus reduces the power consumption. For this purpose, we analyze the power flows of an equivalent electrical circuit of the Hindmarsh–Rose model and replace several nonlinear circuit elements by constant ones. Moreover, we approximate the cubic nonlinearity by three memristors in combination with a negative impedance converter. This negative impedance converter represents the only active circuit element required for the complete circuit, leading to an increased energy efficiency compared to the existing circuit realizations. Simulations verify the circuit’s ability to generate spiking and bursting dynamics comparable to the original Hindmarsh–Rose model.Graphic abstract

Helping networks to get synchronized: Effect of external stimulation

The attempts to evaluate the synchronizability of chaotic systems have shown that additive periodic forcing, as a relevant source of stimuli, significantly impacts multiple forms of synchrony. This paper investigates the complete synchronizability of coupled periodically forced chaotic systems using the master stability function method. Three classic chaotic systems, Lorenz, Chen's, and Hindmarsh-Rose models are employed for this study. The numerical simulations supporting master stability function findings are also reported. The impacts of forcing amplitude and frequency on the critical value of coupling strength at which synchronization occurs are determined. Evidence implies that, as the stimulation is amplified, the chaotic forced systems tend to synchronize at weaker couplings than the autonomous versions. In contrast, high-frequency stimulation is entirely ineffective. The required forcing amplitude is also relative to the system's attractor size.

An Improved Finite-Time and Fixed-Time Stable Synchronization of Coupled Discontinuous Neural Networks.

This article focuses on the finite-time and fixed-time synchronization of a class of coupled discontinuous neural networks, which can be viewed as a combination of the Hindmarsh-Rose model and the Kuramoto model. To this end, under the framework of Filippov solution, a new finite-time and fixed-time stable theorem is established for nonlinear systems whose right-hand sides may be discontinuous. Moreover, the high-precise settling time is given. Furthermore, by designing a discontinuous control law and using the theory of differential inclusions, some new sufficient conditions are derived to guarantee the synchronization of the addressed coupled networks achieved within a finite-time or fixed-time. These interesting results can be seemed as the supplement and expansion of the previous references. Finally, the derived theoretical results are supported by examples with numerical simulations.

Dynamics of a Chain of Interacting Neurons with Nonlocal Coupling, Given by Laplace Operator of Fractional and Variable Orders with Nonlinear Hindmarsh–Rose Model Functions

Dynamics of a Chain of Interacting Neurons with Nonlocal Coupling, Given by Laplace Operator of Fractional and Variable Orders with Nonlinear Hindmarsh–Rose Model Functions

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.

Modes of electrical activities and energy of Hindmarsh–Rose model coupled by memristive synapses

Modes of electrical activities and energy of Hindmarsh–Rose model coupled by memristive synapses

Noise-driven bursting birhythmicity in the Hindmarsh-Rose neuron model.

The stochastic Hindmarsh-Rose model is studied in the parameter region where two bursting limit cycles of different types coexist. We show that under the influence of noise, transitions between basins of attractions appear, which generates stochastic bursting oscillations of mixed modes. The formation of this new regime is accompanied by anti-coherence and coherence resonances as well as by the transition to chaos. We investigate the probabilistic mechanism of the noise-driven bursting birhythmicity using the stochastic sensitivity functions and confidence domains method.