Complex dynamics of a neuron model with discontinuous magnetic induction and exposed to external radiation

Memristor-coupled dual-neuron mapping model: initials-induced coexisting firing patterns and synchronization activities

Synaptic plasticity makes memristors particularly suitable for simulating the connection synapses between neurons that describe magnetic induction coupling. By applying a memristor to the synaptic coupling between two map-based neuron models, a memristor-coupled dual-neuron mapping (MCDN) model is proposed in this article. The MCDN model has a line fixed point set associated with the memristor initial state, which is always unstable for the model parameters and memristor initial state of interest. Complex spiking/bursting firing patterns and their transitions are disclosed using some dynamical analysis means. The numerical results show that these spiking/bursting firings are significantly relied on the memristor initial state, demonstrating the coexistence of firing patterns. Moreover, the initial effects of complete synchronization are explored for the homogeneous MCDN model, and it is clarified that in addition to being related to the coupling strength, the synchronization activities are extremely dependent on the initial states of the memristor and neurons. Finally, these numerical results are confirmed by the FPGA-based hardware experiments.

Dynamical effects of memristive electromagnetic induction on a 2D Wilson neuron model

Electromagnetic induction plays a crucial impact on the firing activity of biological neurons, since it exists along with the mutual effect between membrane potential and ions transport. Flux-controlled memristor is an available candidate in characterizing the electromagnetic induction effect. Different from the previously reported literature, a non-ideal flux-controlled memristor with cosine mem-conductance function is employed to determine the periodic magnetization and leakage flux processes in neurons. Thereafter, a three-dimensional (3D) memristive Wilson (m-Wilson) neuron model is constructed under the consideration of this kind of electromagnetic induction. Numerical simulations are performed by multiple numerical tools, which demonstrate that the 3D m-Wilson neuron model can generate abundant firing activities. Interestingly, coexisting firing activities, antimonotonicity, and firing frequency regulation are discovered under special parameter settings. Furthermore, a PCB-based analog circuit is designed and hardware measurements are executed to verify the numerical simulations. These explorations in numerical and hardware surveys might provide insights to regulate the firing activities by appropriate electromagnetic induction.

Three-dimensional memristive Morris-Lecar model with magnetic induction effects and its FPGA implementation

To characterize the magnetic induction flow induced by neuron membrane potential, a three-dimensional (3D) memristive Morris-Lecar (ML) neuron model is proposed in this paper. It is achieved using a memristor induction current to replace the slow modulation current in the existing 3D ML neuron model with fast-slow structure. The magnetic induction effects on firing activities are explained by the spiking/bursting firings with period-adding bifurcation and periodic/chaotic spiking-bursting patterns, and the bifurcation mechanisms of the bursting patterns are elaborated using the fast-slow analysis method to create two bifurcation sets. In particular, the 3D memristive ML model can also exhibit the homogeneous coexisting bursting patterns when switching the memristor initial states, which are effectively illustrated by the theoretical analysis and numerical simulations. Finally, a digitally FPGA-based hardware platform is developed for the 3D memristive ML model and the experimentally measured results well verify the numerical ones.

Collective dynamics of nonlocally coupled Hindmarsh-Rose neurons modified by magnetic flux

We investigate the dynamics of nonlocally coupled Hindmarsh-Rose neurons, modified by coupling the induced magnetic flux to the membrane potential with a quadratic memristor of strength k. The nonlocal coupling consists of the interaction of each neuron with its neighbors within a fixed radius, which influence the membrane potential of the neuron with coupling intensity σ. For such local dynamics and network of interactions, we investigate how variations of k and σ affect the collective dynamics. We find that when increasing k as well as when increasing σ, coherence typically increases, except for small ranges of these parameters where the opposite behavior can occur. Besides affecting coherence, varying k also affects the pattern of bursts and spikes, namely, for large enough k, burst frequency is augmented, the number and amplitude of the spikes are reduced, and quiescent periods become longer. Results are displayed for an intermediate range of interactions with radius 1/4 of the network size, but we also varied the range of interactions, ranging from first-neighbor to all-to-all couplings, observing in all cases a qualitatively similar impact of induction.

Electromagnetic induction effects on electrical activity within a memristive Wilson neuron model

Neurons can exhibit abundant electrical activities due to physical effects of various electrophysiology environments. The electromagnetic induction flows can be triggered by changes in neuron membrane potential, which can be equivalent to a memristor applying on membrane potential. To imitate the electromagnetic induction effects, we propose a three-variable memristor-based Wilson neuron model. Using several kinetic analysis methods, the memristor parameter- and initial condition-related electrical activities are explored intensively. It is revealed that the memristive Wilson neuron model can display rich electrical activities, including the asymmetric coexisting electrical activities and antimonotonicity phenomenon. Finally, using off-the-shelf discrete components, an analog circuit on a hardware level is implemented to verify the numerically simulated coexisting electrical activities. Studying these rich electrical activities in neurons can build the groundwork to widen the neuron-based engineering applications.

Coexistence of infinitely many patterns and their control in heterogeneous coupled neurons through a multistable memristive synapse

The phenomenon of hidden heterogeneous extreme multistability is rarely reported in coupled neurons. This phenomenon is investigated in this contribution using a model of a 2D FitzHugh-Nagumo neuron coupled with a 3D Hindmarsh-Rose neuron through a multistable memristive synapse. The investigation of the equilibria revealed that the coupled neuron model is equilibrium free and, thus, displays a hidden dynamics. Some traditional nonlinear analysis tools are used to demonstrate that the heterogeneous neuron system is able to exhibit the coexistence of an infinite number of electrical activities involving both periodic and chaotic patterns. Of particular interest, a noninvasive control method is applied to suppress all the periodic coexisting activities, while preserving only the desired chaotic one. Finally, an electronic circuit of the coupled neurons is designed in the PSpice environment and used to further support some results of the theoretical investigations.

Influence of Electric Current and Magnetic Flow on Firing Patterns of Pre-Bötzinger Complex Model

The dynamics of neuronal firing activity is vital for understanding the pathological respiratory rhythm. Studies on electrophysiology show that the magnetic flow is an essential factor that modulates the firing activities of neurons. By adding the magnetic flow to Butera's neuron model, we investigate how the electric current and magnetic flow influence neuronal activities under certain parametric restrictions. Using fast-slow decomposition and bifurcation analysis, we show that the variation of external electric current and magnetic flow leads to the change of the bistable structure of the system and hence results in the switch of neuronal firing pattern from one type to another.

Modulation of Astrocytes on Mode Selection of Neuron Firing Driven by Electromagnetic Induction

Both of astrocytes and electromagnetic induction are magnificent to modulate neuron firing by introducing feedback currents to membrane potential. An improved astro-neuron model considering both of the two factors is employed to investigate their different roles in modulation. The mixing mode, defined by combination of period bursting and depolarization blockage, characterizes the effect of astrocytes. Mixing mode and period bursting alternatively appear in parameter space with respect to the amplitude of feedback current on neuron from astrocyte modulation. However, magnetic flux obviously plays a role of neuron firing inhibition. It not only repels the mixing mode but also suppresses period bursting. The mixing mode becomes period bursting mode and even resting state when astrocytes are hyperexcitable. Abnormal activities of astrocytes are capable to induce depolarization blockage to compose the mixing mode together with bursting mode. But electromagnetic induction shows its strong ability of inhibition of neuron firing, which is also illustrated in the bifurcation diagram. Indeed, the combination of the two factors and appropriate choice of parameters show the great potential to control disorder of neuron firing like epilepsy.

Multiple Firing Patterns in Coupled Hindmarsh-Rose Neurons with a Nonsmooth Memristor

A model is introduced by coupling two three-dimensional Hindmarsh-Rose models with the help of a nonsmooth memristor. The firing patterns dependent on the external forcing current are explored, which undergo a process from adding-period to chaos. The stability of equilibrium points of the considered model is investigated via qualitative analysis, from which it can be gained that the model has diversity in the number and stability of equilibrium points for different coupling coefficients. The coexistence of multiple firing patterns relative to initial values is revealed, which means that the referred model can appear various firing patterns with the change of the initial value. Multiple firing patterns of the addressed neuron model induced by different scales are uncovered, which suggests that the discussed model has a multiscale effect for the nonzero initial value.

Complex bifurcation analysis and synchronization optimal control for Hindmarsh-Rose neuron model under magnetic flow effect

In this contribution, the complex behaviour of the Hindmarsh-Rose neuron model under magnetic flow effect (mHR) is investigated in terms of bifurcation diagrams, Lyapunov exponent plots and time series when varying only the electromagnetic induction strength. Some exciting phenomena are found including, for instance, various firings patterns by applying appropriate magnetic strength and Hopf-fold bursting through fast-slow bifurcation. In addition to this, the interesting phenomenon of Hopf bifurcation is examined in the model. Thus, we prove that Hopf bifurcation occurs in this memristor-based HR neuron model when an appropriately chosen magnetic flux varies and reaches its critical value. Furthermore, one of the main results of this work was the optimal control approach to realize the synchronization of two mHR. The main advantage of the proposed optimal master-slave synchronization from a control point of view is that, in the practical application, the electrical activities (quiescent, bursting, spiking, period and chaos states) of a neuron can be regulated by a pacemaker (master) associated with biological neuron (slave) to treat some diseases such as epilepsy. A suitable electronic circuit is designed and used for the investigations. PSpice based simulation results confirm that the electrical activities and synchronization between coupled neurons can be modulated by electromagnetic flux.

Energy dependence on discharge mode of Izhikevich neuron driven by external stimulus under electromagnetic induction

Energy supply plays a key role in metabolism and signal transmission of biological individuals, neurons in a complex electromagnetic environment must be accompanied by the absorption and release of energy. In this paper, the discharge mode and the Hamiltonian energy are investigated within the Izhikevich neuronal model driven by external signals in the presence of electromagnetic induction. It is found that multiple electrical activity modes can be observed by changing external stimulus, and the Hamiltonian energy is more dependent on the discharge mode. In particular, there is a distinct shift and transition in the Hamiltonian energy when the discharge mode is switched quickly. Furthermore, the amplitude of periodic stimulus signal has a greater effect on the neuronal energy compared to the angular frequency, and the average Hamiltonian energy decreases when the discharge rhythm becomes higher. Based on the principle of energy minimization, the system should choose the minimum Hamiltonian energy when maintaining various trigger states to reduce the metabolic energy of signal processing in biological systems. Therefore, our results give the possible clues for predicting and selecting appropriate parameters, and help to understand the sudden and paroxysmal mechanisms of epilepsy symptoms.