Dynamics explore of an improved HR neuron model under electromagnetic radiation and its applications

The influence of electromagnetic field to neuron firing rhythm is not negligible. In order to investigate the behavior mechanism, a five-dimensional neuron model based on the Faraday's law of electromagnetic induction is improved by introducing magnetic flux variables and electric field variables on the three-dimensional Hindmarsh–Rose (HR) neuron model, and then, its rich dynamics and application in image encryption are discussed. Specifically, the equilibrium point distribution is analyzed using Matcont software and it is found that there are subcritical Hopf bifurcation and coexisting mode firing first. Second, numerical simulations are performed in terms of two-parameter bifurcation, ISI bifurcation, the maximum Lyapunov exponent and firing sequences, and the experimental results show that the new model exhibits various firing rhythms. The rich dynamic behaviors make the model more suitable for application in image encryption. So in the end, a grayscale image encryption scheme containing five parts called sparse, compression calculation, forward diffusion, rank scrambling and backward diffusion is designed by combining with the compressive sensing theory. The security analysis results show that the designed encryption scheme not only has excellent compression performance and high security, but also displays faster encryption speed. That is to say, the algorithm can be applied to the field of real encryption owning to the advantages of the lower costs of data transmission and higher efficiency of encryption. It is worth mentioning that the influence of different dimensional compression methods on the encryption and reconstruction effects is analyzed for the first time. The research results of this paper provide some ideas for perfecting the neuron model, revealing the influence of electromagnetic field on biological nervous system, and the excellent performance of the new neuron model provides theoretical guidance and experimental basis for the practical application of digital image encryption.

     

Practical synchronization of second-order nonautonomous systems with parameter mismatch and its applications

This paper is concerned with robust practical synchronization for general second-order nonautonomous systems with parameter mismatch. Some simple yet general algebraic criteria are derived based on practical stability theory of nonautonomous dynamical systems. A?distinctive feature of this work is that the parameter mismatch cannot only be existed in system parameters, but also in external excitation ones. Furthermore, the obtained results are applied to a typical horizontal platform system and the representative forced Van der Pol oscillator. Subsequently, numerical simulations demonstrate the effectiveness of the criteria and the robustness of the control technique.     

Energy-efficient firing patterns with sparse bursts in the Chay neuron model

Nonlinear Dynamics - The energy efficiency of neural signal transmission is thought to be an important constraint in the nervous system. It is generally measured as the energy consumed per unit of...     

Generalized quantized intermittent control with adaptive strategy on finite-time synchronization of delayed coupled systems and applications

Nonlinear Dynamics - This paper is concerned with the finite-time synchronization problem of coupled drive-response systems with time-varying delays via quantized adaptive aperiodically...     

Synchrony and lag synchrony on a neuron model coupling with time delay

A neuron model of the Morris and Lecar form is investigated, which is composed of two individuals and is considered to be functioned by the gap junction coupling. When the level of the reversal potential in the calcium ion channel is small, neurons adjust their activities to the common asymptotic states. However, if we increase the level of the reversal voltage in the calcium ion channel, the exact synchrony firing of neurons is produced. Patterns of synchrony activity and the stability are observed to vary with the choice of time delay, which also enhances the multi-variety of the spike bursting firing rhythm. The lag synchrony of time trajectories of the voltage is illustrated near the boundary of the synchrony regime.     

Dynamical analysis of an improved FitzHugh-Nagumo neuron model with multiplier-free implementation

The cubic-polynomial nonlinearity with N-shaped curve plays a crucial role in generating abundant electrical activities for the original FitzHugh-Nagumo (FHN) neuron model. The pioneer FHN neuron model is efficient in theoretical analysis and numerical simulation for these abundant electrical activities, but analog multipliers are indispensable in hardware implementation since the involvement of cubic-polynomial nonlinearity. Analog multiplier goes against the circuit integration of FHN neuron model due to its huge implementation costs. To avoid the involvement of analog multiplier in hardware implementation, a nonlinear function possessing N-shaped curve and multiplier-free implementation is presented in this paper. To confirm the availability of this nonlinear function in generating electrical activities, numerical simulations and hardware experiments are successfully executed on an improved two-dimensional (2D) FHN neuron model with externally applied stimulus. The results demonstrate that the improved FHN neuron model can generate rich electrical activities of periodic spiking behavior, chaotic behavior, and quasi-periodic behavior. Analog circuit implementation without any multiplier and its hardware experiment show the availability of the proposed nonlinear function, which is appropriate for analog circuit implementation of FHN neuron-based neuromorphic intelligence.

     

Impulsive pinning complex dynamical networks and applications to firing neuronal synchronization

The primary objective of this paper is to propose a new approach for analyzing pinning stability in a complex dynamical network via impulsive control. A?simple yet generic criterion of impulsive pinning synchronization for such coupled oscillator network is derived analytically. It is shown that a single impulsive controller can always pin a given complex dynamical network to a homogeneous solution. Subsequently, the theoretic result is applied to a small-world (SW) neuronal network comprised of the Hindmarsh?CRose oscillators. It turns out that the firing activities of a single neuron can induce synchronization of the underlying neuronal networks. This conclusion is obviously in consistence with empirical evidence from the biological experiments, which plays a significant role in neural signal encoding and transduction of information processing for neuronal activity. Finally, simulations are provided to demonstrate the practical nature of the theoretical results.     

Effect of spatially correlated noise on stochastic synchronization in globally coupled FitzHugh-Nagumo neuron systems

The phenomenon of stochastic synchronization in globally coupled FitzHugh-Nagumo (FHN) neuron system subjected to spatially correlated Gaussian noise is investigated based on dynamical mean-field approximation (DMA) and direct simulation (DS). Results from DMA are in good quantitative or qualitative agreement with those from DS for weak noise intensity and larger system size. Whether the consisting single FHN neuron is staying at the resting state, subthreshold oscillatory regime, or the spiking state, our investigation shows that the synchronization ratio of the globally coupled system becomes higher as the noise correlation coefficient increases, and thus we conclude that spatial correlation has an active effect on stochastic synchronization, and the neurons can achieve complete synchronization in the sense of statistics when the noise correlation coefficient tends to one. Our investigation also discloses that the noise spatial correlation plays the same beneficial role as the global coupling strength in enhancing stochastic synchronization in the ensemble. The result might be useful in understanding the information coding mechanism in neural systems.     

Complete dynamical analysis of a neuron model

In-depth understanding of the generic mechanisms of transitions between distinct patterns of the activity in realistic models of individual neurons presents a fundamental challenge for the theory of applied dynamical systems. The knowledge about likely mechanisms would give valuable insights and predictions for determining basic principles of the functioning of neurons both isolated and networked. We demonstrate a computational suite of the developed tools based on the qualitative theory of differential equations that is specifically tailored for slow–fast neuron models. The toolkit includes the parameter continuation technique for localizing slow-motion manifolds in a model without need of dissection, the averaging technique for localizing periodic orbits and determining their stability and bifurcations, as well as a reduction apparatus for deriving a family of Poincaré return mappings for a voltage interval. Such return mappings allow for detailed examinations of not only stable fixed points but also unstable limit solutions of the system, including periodic, homoclinic and heteroclinic orbits. Using interval mappings we can compute various quantitative characteristics such as topological entropy and kneading invariants for examinations of global bifurcations in the neuron model.     

HR2钢及几种铁基材料的冲击相变行为

利用双灵敏度VISAR测量了抗氢钢HR2、工业纯铁DT2和铁锰镍合金FeMnNi在一维应变冲击载荷下的自由面速度历史,结合受载样品的回收分析对其动载行为和断裂表现进行了分析。研究表明,在实验加载压力范围内DT2和FeMnNi样品的自由面速度历史呈现包括相变波在内的典型三波结构,而对HR2钢,尽管金相分析显示其加载前后样品的相组织已发生变化,但速度剖面呈现的仅是典型的弹塑性双波结构。分析认为溶质材料成分和初始相组织是无相变波的主要原因。从冲击相变和卸载逆相变角度解释了在等厚靶碰撞时DT2和FeMnNi材料中出现的多重层裂、浅表层裂现象。     

Complex function projective synchronization of complex chaotic system and its applications in secure communication

To develop secure communication, the paper presents complex function projective synchronization (CFPS) of complex chaotic systems. Aimed to coupled complex chaotic system, the control law is derived to make the complex state vectors asymptotically synchronize up to a desired complex function matrix. Based on CFPS, a novel communication scheme is further designed in theory. Its main idea is chaotic masking in essence, but the transmitted signal is the derivative of the product of the information signal and chaotic signal. As the complex scaling functions are arbitrary and more unpredictable than real scaling functions, and the product and derivative operations of complex numbers are complicated, the possibility that an interceptor extracts the information from the transmitted signal is greatly reduced. The communication system can transmit analog signal and digital symbols with fast transmission and high security, especially low bit-error rate and the strong robustness to noise for digital symbols. The corresponding numerical simulations are performed to verify and illustrate the analytical results.     

Parameter-dependent synchronization of coupled neurons in cold receptor model

In this paper, synchronization in two coupled neurons with spiking, bursting and chaos firings is investigated as the coupling strength gets increased. Synchronization state can be identified by means of the bifurcation diagram, the correlation coefficient and ISI-distance. It is illustrated that the coupled neurons can exhibit different types of synchronization state when the coupling strength increases. The different synchronization processes appear similar, but their detailed processes are different depending on the parameter values. The synchronization of neuronal network with two different network connectivity patterns is also studied. It is shown that chaotic and high period pattern are more difficult to get complete synchronization than the situation in single spike and low period pattern. It is also demonstrated that the synchronization status of multiple neurons is dependent on the network connectivity patterns. These results may be instructive to understand synchronization in neuronal systems.     

Invariant spectral foliations with applications to model order reduction and synthesis

Nonlinear Dynamics - The paper introduces a technique that decomposes the dynamics of a nonlinear system about an equilibrium into low-order components, which then can be used to reconstruct the...     

Global multistability and analog circuit implementation of an adapting synapse-based neuron model

This paper proposes a MEMS resonant pressure sensor through implementing an out-of-plane repulsive (levitation) force to enhance the sensor detection threshold and consequently widen its sensing range. 2D and 3D finite-element simulations are conducted and compared to some available experimental data. The simulated results show an increase in the generated levitation force as outstanding merit owing to the added side upper electrodes. The levitation force is then further increased by lateral spacing optimization in association with the assumed applied voltage, which decreases the overall size (footprint) as well. The dynamical behavior around the static equilibrium is first numerically solved using the so-called shooting technique and then compared with an available online simulation tool: the “Matcont” package. The simulated results prove the capability of the online simulator to capture the dynamic response of the resonant micro-sensor when approaching its respective bifurcation points where the stable and unstable branches collide, when in contrary, the shooting technique failed to get the dynamic responses when passing by these bifurcations. Thanks to the fast converging outcomes of the “Matcont” online simulation equipped with simultaneous stability analysis, a comprehensive analysis of the micro-sensor dynamical response is conducted. Three sensing mechanisms as: measurements of frequency shift, amplitude alternation, and amplitude rise/fall near a bifurcation region are evaluated and characterized. Along with enumerating the strengths of the proposed sensor over the conventional capacitive pressure sensors, the advantage of measuring the amplitude rise/fall near the corresponding bifurcation region comparing to the two other sensing mechanisms is detailed, and its possible failure for performance repeatability is resolved by means of the slow-varying frequency sweep. Unlike the traditional parallel-plate configuration in which only one-side frequency shift is observed, in this proposed design, two-sides frequency shift is detected, and accordingly, the reinitialization is categorized based on that. As compared to the conventional MEMS pressure sensor, this revisited design equipped with the suggested sensing mechanism offers wider tunability and sensing range, resolution power enhancement, and simplification of the signal processing circuit.

     

Analysis of spatially extended excitable Izhikevich neuron model near instability

The dynamic response and bifurcations of high-dimensional systems endowed with hysteretic restoring forces in all degrees of freedom are investigated. Two types of hysteresis models are considered, namely the Bouc–Wen model and a differential version of the so-called exponential model of hysteresis. The numerical technique tailored for tackling high-dimensional hysteretic systems is based on an enhanced pathfollowing approach based on the Poincaré map. In particular, a five-dof mass-spring-damper-like system, with each rheological element described by the Bouc–Wen or the exponential model of hysteresis enriched by cubic and quintic nonlinear elastic terms, is investigated and a rich variety of nonlinear responses and bifurcations is found and discussed.

     

The alternating between complete synchronization and hybrid synchronization of hyperchaotic Lorenz system with time delay

The various cases of synchronization in two identical hyperchaotic Lorenz systems with time delay are studied. Based on Lyapunov stability theory, the sufficient conditions for achieving synchronization of two identical hyperchaotic Lorenz systems with time delay are derived, and a simple scheme only with a single linear controller is proposed. When the parameters in the response system are known, the alternating between complete synchronization and hybrid synchronization (namely, coexistence of antiphase and complete synchronization) is observed with the control feedback gain varying. Furthermore, when the parameters in the response system are unknown, for the same feedback controller, the complete synchronization and the hybrid synchronization can be obtained, respectively, as the associated parameters updated laws of the unknown parameters are chosen. Numerical simulation results are presented to demonstrate the proposed chaos synchronization scheme.     

Stability and bifurcation analysis in the coupled HR neurons with delayed synaptic connection

Nonlinear Dynamics - This paper presents stability and bifurcations of two synaptically coupled identical Hindmarsh–Rose neurons with one time delay. The parameters we choose contribute to...