Hindmarsh Rose Research Articles

Symmetry breaker governs synchrony patterns in neuronal inspired networks.

Experiments in the human brain reveal switching between different activity patterns and functional network organization over time. Recently, multilayer modeling has been employed across multiple neurobiological levels (from spiking networks to brain regions) to unveil novel insights into the emergence and time evolution of synchrony patterns. We consider two layers with the top layer directly coupled to the bottom layer. When isolated, the bottom layer would remain in a specific stable pattern. However, in the presence of the top layer, the network exhibits spatiotemporal switching. The top layer in combination with the inter-layer coupling acts as a symmetry breaker, governing the bottom layer and restricting the number of allowed symmetry-induced patterns. This structure allows us to demonstrate the existence and stability of pattern states on the bottom layer, but most remarkably, it enables a simple mechanism for switching between patterns based on the unique symmetry-breaking role of the governing layer. We demonstrate that the symmetry breaker prevents complete synchronization in the bottom layer, a situation that would not be desirable in a normal functioning brain. We illustrate our findings using two layers of Hindmarsh-Rose (HR) oscillators, employing the Master Stability function approach in small networks to investigate the switching between patterns.

Dynamics of Hindmarsh–Rose diffusive system

Dynamics of Hindmarsh–Rose diffusive system

Firing patterns transitions and resonance effects of the extended Hindmarsh-Rose neural model with Gaussian noise and transcranial magneto-acousto-electrical stimulation

Considering the fact that the typical three-variable Hindmarsh-Rose(HR) neural model has limitations in describing the complex non-linear features and precise behavior patterns of neuron, the influences of transcranial magneto-acousto-electrical stimulation(TMAES) on firing patterns and resonance effects are analyzed based on an extended HR neural model in this paper. Obtained results show that TMAES can induce transitions in the firing patterns of extended HR neuron, such as spiking and multi-periodic bursting state, etc If appropriate parameters are selected, the multimodal discharge modes can also be observed. Coefficient of variation is calculated to further investigate the effect of TMAES and Gaussian white noise on the firing rhythm of extended HR neuron, and relevant results indicate that TMAES can induce coherent resonance phenomena in HR neuronal systems similar to the effects of Gaussian white noise, which reveals a new mechanism of coherent resonance induced by TMAES. Further more, TMAES can also regulate coefficient of variation to exhibit anti-coherent resonance and multiple anti-coherent resonance structures, exhibiting richer regulatory functions than Gaussian white noise in regulating neuronal firing rhythm. This study seeks to enhance the understanding of the processes that influence the firing patterns and coherence degree of neuron under TMAES in neuroses or psychoses.

Spatiotemporal patterns in a 2D lattice of Hindmarsh–Rose neurons induced by high-amplitude pulses

We present numerical results for the effects of influence by high-amplitude periodic pulse series on a network of nonlocally coupled Hindmarsh–Rose neurons with 2D geometry of the topology. We consider the case when the pulse amplitude is larger than the amplitude of oscillations in the autonomous network for a wide range of pulse frequencies. An initial regime in the network is a spiral wave chimera. We show that the effects of external influence strongly depend on a balance between the pulse frequency and frequencies of the spectral peaks of the autonomous network. Except for the destructive role of the pulses, when they lead to loss of stability of the initial regime, we have also revealed a constructive role. We have found for the first time the emergence of a new type of multi-front spiral waves, when the wavefront represents a set of several close fronts, and the wave dynamics are significantly different from common spiral waves: neurons oscillate independently to the wave rotation, the rotation velocity is in many times less than for the common spiral wave, etc. We have also discovered several types of cluster spatiotemporal structures induced by the pulses.

Transition and bifurcation mechanism of firing activities in memristor synapse-coupled Hindmarsh–Rose bi-neuron model

Memristor, especially the locally active one, is widely used in emulating the synapse-inspired activities in neural networks, in which the connection between memristor properties and neuronal electrical activities requires further investigation. In this paper, a bi-neuron model is constructed by bi-directionally connecting a locally active memristor between the membrane potentials of two deterministic 3D HR neuron models. Complex spiking/bursting firing activities and their transitions are disclosed under different memristor control parameters. The bifurcation mechanisms of the revealed synchronous and asynchronous firing activities are explored inside each individual neuron by taking the externally input state variables as modulation parameters. These results demonstrate the crucial effect of the locally active memristor synapse on firing activities of its coupled network. FPGA-based digital circuit experiment is finally performed to verify the numerical results. This research is beneficial to understanding, control and application of firing activities in neural networks.

Memristors-coupled neuron models with multiple firing patterns and homogeneous and heterogeneous multistability

Abstract Memristors are extensively used to estimate the external electromagnetic stimulation and synapses for neurons. In this paper, two distinct scenarios, i.e., an ideal memristor serves as external electromagnetic stimulation and a locally active memristor serves as a synapse, are formulated to investigate the impact of a memristor on a two-dimensional Hindmarsh–Rose neuron model. Numerical simulations show that the neuronal models in different scenarios have multiple burst firing patterns. The introduction of the memristor makes the neuronal model exhibit complex dynamical behaviors. Finally, the simulation circuit and DSP hardware implementation results validate the physical mechanism, as well as the reliability of the biological neuron model.

Fractional-order heterogeneous neuron network based on coupled locally-active memristors and its application in image encryption and hiding

Synaptic crosstalk significantly influences neural firing in the brain. Locally-active memristors can effectively emulate neural network synapses and have a significant importance in neural network research. This paper designs a tristable locally-active memristive model and presents a novel fractional-order (FO) heterogeneous neuron network. This neural network consists of Hindmarsh-Rose (HR) neuron and FitzHugh-Nagumo (FHN) neuron, which are connected by coupling FO locally-active memristors. The research found that changes in the order of different dimensions have a significant effect on the neural network firing through the three-parameter bifurcation diagram. Moreover, it is found that the locally-active memristor as a synapse can affect the coexistence firing behavior of the network. The complex dynamics have been studied numerically by using phase diagrams, Lyapunov exponent spectrum, bifurcation diagram and extreme multistability can be found. In particular, the system can generate a complex bursting behavior in the presence of an external current. In order to verify the accuracy of the simulation, the phase diagram of FO heterogeneous neuron network is implemented by STM32 microcontroller, and results of the experiments are in great agreement with results of the numerical simulations. Finally, an image encryption and hiding method based on FO heterogeneous neuron network and discrete wavelet transform (DWT) is proposed. The experimental results demonstrate that the encryption and hiding scheme has excellent security and strong robustness.

A Hindmarsh–Rose neuron model with electromagnetic radiation control for the mechanical optimization design

This paper proposes a Hindmarsh–Rose(HR) neuron model controlled by electromagnetic radiation to solve the mechanical optimization design problem. A novel memristor for simulating electromagnetic radiation is established to control the dynamical behavior of HR neuron models. By analyzing the HR model and using the numerical analysis methods of phase portrait, bifurcation diagram, Lyapunov exponent and spectral entropy (SE) complexity, the HR model is shown to have a hidden attractor and rich chaotic dynamics. Then, a chaotic optimization algorithm based on HR neuron model is designed to solve the mechanical optimization design of tension/compression coil springs and pressure vessels. The chaotic sequence of this algorithm which has high-quality pseudo-random number, has stronger global search ability. Simulation of two mechanical optimization design problems in comparison with some well-known optimization algorithms demonstrates the superiority of the HR in the solution quality.

Effects of external stimuli on the dynamics of deterministic and stochastic Hindmarsh–Rose neuron models

Effects of external stimuli on the dynamics of deterministic and stochastic Hindmarsh–Rose neuron models

Predefined finite time anti-phase synchronization studies of Hindmarsh–Rose neuron networks

Predefined finite time anti-phase synchronization studies of Hindmarsh–Rose neuron networks

Constructing Memristive Hindmarsh–Rose Neuron with Countless Coexisting Firings

Memristor synapses have been widely introduced into neuronal models to investigate the effects of external magnetic fields. However, there is a relative lack of research on the external-induced electric fields in neurons. In this paper, a 4D-memristive Hindmarsh–Rose neuron model is constructed by introducing a memristor and an electric field variable, which can generate complex neural firing. Notably, numerical simulations reveal that the initial conditions of the memristor can induce different firing patterns, exhibiting a unique fractal structure in the basin of attractions. Remarkably, the offset parameters of the internal variables of the neuron can be canceled out so that the offset boosting of the variables can be achieved according to the initial values, giving rise to an uncountably many hidden attractors with homogeneous multistability. This model provides the first example of generating uncountably many attractors in a memristive neuron model without relying on trigonometric functions, significantly advancing our understanding of neuronal dynamics. Finally, a digital circuit is designed and implemented on the RISC-V platform to verify the numerical simulation and theoretical analysis. The findings of this study have a certain implication for the development of advanced neuromorphic computing systems and the understanding of complex neuronal behaviors in the presence of external electric fields.

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

Investigation of Synchronization Control of the Memristive/Resistive-Coupled Neural Network with Noise Effect

This study comprehensively investigates synchronization control of the memristive- and resistive-coupled neural network with noise effect. In this context, a sub-network is constructed with three chaotic memristive Hindmarsh–Rose neurons coupled by the memristive synapses. Then, two equivalent sub-networks are linked by the diffusive resistive synapse under a distinctive global network structure including two sub-networks. Thus, a double (memristive/resistive) control mechanism is used to achieve the synchronization state. The first mechanism is the memristive synaptic coupling in each sub-network, and the second one is the diffusive resistive coupling between two sub-networks constructing the global network. The synchronization between the neurons is proven theoretically through the Lyapunov stability and Lipschitz theorems and this proof process is verified with numerical experiments. According to the theoretical and numerical results, by adjusting memristive/resistive synaptic coupling weights, a synchrony behavior is generated successfully in these sub-networks and global networks. Additionally, this paper also handles the Gaussian white noise effect on the global network to examine continuity capability and stability of synchronization. Two different frameworks are built by applying the noise with multiple noise power levels and periods to (i) one of the resistive coupling neurons in each sub-network directly and (ii) one neuron in a sub-network without direct contact with the other sub-network. With these two characteristic designs, it is proven that the second design provides more robust characteristics since it utilizes the double control mechanism, which enhances the stability throughout external interferences enabling the network to sustain synchronous states.

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.

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.

Biological neuron modeling based on bifunctional memristor and its application in secure communication

In recent years, memristors have shown great potential in building artificial neural networks. Many researchers have worked on improving and innovating the design of memristors. The bifunctional memristor proposed in this paper provides new ideas for establishing artificial neural networks. And a novel second-order memristor Hindmarsh–Rose neuron (SOM-HR) is constructed on this basis. The SOM-HR model can well simulate the dynamical behavior of the memristive autapse HR neuron under electromagnetic radiation (EMR), and many types of firing patterns, coexisting firing patterns and state transition are found. In addition, the correctness of the numerical simulation is verified by circuit simulation and digital signal processor (DSP) implementation. Finally, the chaotic sequences generated by this model are used for image encryption, which guarantees the security of the encryption scheme. The results of the study provide a reference for construction and application of complex neural network.

Exploring the geometry of the bifurcation sets in parameter space

By studying a nonlinear model by inspecting a p-dimensional parameter space through (p-1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(p-1)$$\\end{document}-dimensional cuts, one can detect changes that are only determined by the geometry of the manifolds that make up the bifurcation set. We refer to these changes as geometric bifurcations. They can be understood within the framework of the theory of singularities for differentiable mappings and, in particular, of the Morse Theory. Working with a three-dimensional parameter space, geometric bifurcations are illustrated in two models of neuron activity: the Hindmarsh–Rose and the FitzHugh–Nagumo systems. Both are fast-slow systems with a small parameter that controls the time scale of a slow variable. Geometric bifurcations are observed on slices corresponding to fixed values of this distinguished small parameter, but they should be of interest to anyone studying bifurcation diagrams in the context of nonlinear phenomena.

Multiple firing patterns, energy conversion and hardware implementation within Hindmarsh-Rose-improved neuron model

The transmission of information between neurons is accomplished in living organisms through synapses. The memristor is an electronic component that simulates the tunability of the strength of biological synaptic connections in artificial neural networks. This article constructs a novel type of locally active memristor and verifies by nonlinear theoretical analysis, locally active analysis and circuit simulation. The designed memristor is simulated as a biological autapse of Hindmarsh-Rose(HR) neuron to obtain the improved HR neuron model of memristive autapse, and the Hamilton energy is obtained according to Helmholtz theorem. By varying the external forcing current and the memristive autapse strength, this article analyses the changes of the Hamilton energy and explores its self-excited and hidden firing behavior. The analog circuit simulation and digital circuit implementation of the HR model confirm the consistency between the mathematical model and the actual behavior, which can advance the field of neuroscience and artificial intelligence.

Firing pattern transition of fractional-order memristor-coupled Hindmarsh–Rose neurons model and its medical image encryption for region of interest

Firing pattern transition of fractional-order memristor-coupled Hindmarsh–Rose neurons model and its medical image encryption for region of interest

Coexisting firing patterns and attractor selection in memristive synapse coupled heterogeneous neurons

In this paper, we present a novel heterogeneous neuron network involving the coupling of a two-dimensional (2D) continuous Rulkov model with a 2D Hindmarsh-Rose (HR) neuron via memristive synapse. The present memristive coupled neuron network can produce an infinite number of coexisting hidden attractors with the same shape but located at different positions in the phase space, resulting in the interesting phenomenon of hidden homogeneous extreme multistability. Firstly, we study complex dynamical behaviors in detail through bifurcation diagrams, Lyapunov exponents, time series and phase portraits. Secondly, to select the desired firing pattern, a control method based on the feedback term is applied to the model. It is observed that the addition of this space-dependent feedback term to the dynamic equation of this model effectively eliminates all undesired firing patterns among the coexisting ones, and drives the heterogeneous neuron network to transition from coexisting hidden firing patterns to the expected firing pattern. Finally, Multisim circuit simulation is performed and the results are in line with numerical simulation.