Synchronization in a Multiplex Network of Nonidentical Fractional-Order Neurons

Fractional-order neuronal models that include memory effects can describe the rich dynamics of the firing of the neurons. This paper studies synchronization problems in a multiple network of Caputo–Fabrizio type fractional order neurons in which the orders of the derivatives in the layers are different. It is observed that the intralayer synchronization state occurs in weaker intralayer couplings when using nonidentical fractional-order derivatives rather than integer-order or identical fractional orders. Furthermore, the needed interlayer coupling strength for interlayer near synchronization decreases for lower fractional orders. The dynamics of the neurons in nonidentical layers are also considered. It is shown that in lower fractional orders, the neurons’ dynamics change to periodic when the near synchronization state occurs. Moreover, decreasing the derivative order leads to incrementing the frequency of the bursts in the synchronization manifold, which is in contrast to the behavior of the single neuron

Effect of Noise variance in spiral wave suppression for a multi-layered neuron model with flux coupling modelled using a memristor

Dynamics of multi-layered neuronal network are challenging and spiral wave suppression is vital particularly in biological systems such as cortical tissue in brain, heart muscles etc., In this study, one-, two- and three-layer neuronal network of an exponential flux memristor-based Morris-Lecar neuron model subjected to low-frequency electromagnetic field (MLELF) is considered and the influence of noise variance in spiral wave suppression is investigated. A Box- Muller type Gaussian noise is used as stimulation and the influence of noise variance on neuronal network is studied. The results exposed the multilayer neuronal network influenced much by a very low noise variance on spiral wave suppression while compared with the single-layer network. As increase in noise variance, the dynamics of the spiral wave changes significantly and ended with turbulence. The study highlighted the spiral waves can be potentially suppressed even the network is under higher frequency external electric field using noise variance

Driven Force Induced Bifurcation Delay on the Chaotic Financial System

To understand the variations in the financial characteristics, we examine the dynamical behaviors by considering the chaotic financial model with external force. First, the dynamical characteristics are analyzed by introducing the external driven force in the price index with commodity demand. We discover that the presence of an external force causes the alternate occurrence of oscillatory and steady states as a function of time. Interestingly, we find the existence of bifurcation delay (BD) during the transition from oscillatory (OS) to steady state (SS) or vice versa. Bifurcation delay is a phenomenon in which the bifurcation does not occur at the actual bifurcation point but rather at a later time, which is referred to as bifurcation delay. To confirm the delay in bifurcation, we estimate the actual bifurcation point and compare it to the observed bifurcation transition. Furthermore, to understand the variations in the bifurcation delay, we estimate the delay time between each consecutive cycle and find random fluctuations in the BD. Following that, the BD is virtualized via a transformed phase portrait. In addition, we show decreasing the value of average BD while increasing the frequency of external forcing. Second, the presence of BD is explored by incorporating external forces into the investment demand with unit investment cost. We discover the existence of a similar phenomenon with a constant bifurcation delay

Effects of noise on the wave propagation in an excitable media with magnetic induction

In this paper, we investigate the wave propagation phenomenon and network dynamics of an improved Hindmarsh–Rose neuron model considered with magnetic induction. The dynamical properties of the improved neuron model in discussed with the help of eigenvalues, Lyapunov exponents and bifurcation plots. A simple comparison between the exponential flux model and quadratic flux model is investigated and shown that the exponential flux model could show behavior like the quadratic model with its memductance monotonically increasing or decreasing depending on the polarity of the voltage. In the network dynamics investigation, we have considered two additional external disturbances such as the noise and flux excitation. A mathematical model of a lattice array with Box–Mueller type random noise and a sinusoidal periodic flux excitation is defined. The wave propagation phenomenon in the presence of noise is investigated using the noise variance as the control parameter. We could show that when the noise is applied to the network for the entire simulation time, the spiral waves are effectively suppressed for very low noise variance values

Analysis of FBMC waveform for 5g network based smart hospitals

Nowadays, many prevalent frameworks for medical care have been projected, studied, and implemented. The load and challenges of traditional hospitals are increasing daily, leading to inefficient service in the health system. Smart hospitals based on advanced techniques play a crucial part in advancing the health services of rural people. It spares the time and money involved in travel, and patient medical reports can be shared instantly with the experts regardless of geographical constraints. Currently, the role of technology in hospitals is limited due to various restrictions, such as the obtainability of a high spectrum, low latency, and high-speed network. In this paper, we focused on the implementation of an advanced waveform with high spectral performance. Filer Bank Multi-Carrier (FBMC) is considered a strong contender for the upcoming 5G-centered smart hospitals due to its high data rate, no leakage of the spectrum, and less sensitivity to frequency error. In addition, a comparison of the spectral utilization of orthogonal frequency division multiplexing (OFDM) and FBMC in terms of bit error rate (BER), peak power (PP), power spectral density (PSD), noise-PSD, capacity and magnitude, and phase response is illustrated. Numerical results show that the FBMC achieved a throughput gain of 1 dB and its spectral performance is better than the OFDM; hence, it is a better choice for the proposed application compared to the current standard OFDM

A New Memristive Neuron Map Model and Its Network’s Dynamics under Electrochemical Coupling

A memristor is a vital circuit element that can mimic biological synapses. This paper proposes the memristive version of a recently proposed map neuron model based on the phase space. The dynamic of the memristive map model is investigated by using bifurcation and Lyapunov exponents’ diagrams. The results prove that the memristive map can present different behaviors such as spiking, periodic bursting, and chaotic bursting. Then, a ring network is constructed by hybrid electrical and chemical synapses, and the memristive neuron models are used to describe the nodes. The collective behavior of the network is studied. It is observed that chemical coupling plays a crucial role in synchronization. Different kinds of synchronization, such as imperfect synchronization, complete synchronization, solitary state, two-cluster synchronization, chimera, and nonstationary chimera, are identified by varying the coupling strengths

A New Memristive Neuron Map Model and Its Network’s Dynamics under Electrochemical Coupling

A memristor is a vital circuit element that can mimic biological synapses. This paper proposes the memristive version of a recently proposed map neuron model based on the phase space. The dynamic of the memristive map model is investigated by using bifurcation and Lyapunov exponents’ diagrams. The results prove that the memristive map can present different behaviors such as spiking, periodic bursting, and chaotic bursting. Then, a ring network is constructed by hybrid electrical and chemical synapses, and the memristive neuron models are used to describe the nodes. The collective behavior of the network is studied. It is observed that chemical coupling plays a crucial role in synchronization. Different kinds of synchronization, such as imperfect synchronization, complete synchronization, solitary state, two-cluster synchronization, chimera, and nonstationary chimera, are identified by varying the coupling strengths

On the dynamics of a system of two coupled van der Pol oscillators subjected to a constant excitation force: effects of broken symmetry

We consider the dynamics of a system of two coupled van der Pol oscillators whose (inversion) symmetry is broken by a constant excitation force. We investigate the bifurcation structures of the system both with respect to its parameters and the intensity of the excitation force as well using numerical methods. It is found that the forced system experiences rich and complex bifurcation patterns including period-doubling, crises, coexisting bifurcation branches, and hysteresis. Due to the absence of symmetry, the system develops relatively much more complex dynamics which are reflected by the coexistence of multiple (i.e. two, three or four) asymmetric attractors. Moreover, one of the most interesting and striking features of the system considered in this work is the coexistence of periodic and chaotic bubbles of bifurcation for some suitable parameter ranges. This later phenomenon was not reported previously and thus deserves dissemination

Infinitely many coexisting hidden attractors in a new hyperbolic-type memristor-based HNN

In this article, a new model of Hopfield Neural Network (HNN) with two neurons considering a synaptic weight with a hyperbolic-type memristor is studied. Equilibrium points analysis shows that the system has an unstable line of equilibrium in the absence of the external stimuli (i.e. $$I_{1} =0)$$ and presents no equilibrium point in the presence of the external stimuli (i.e. $$I_{1} \ne 0)$$; hence the model admits hidden attractors. Analyses are carried out for both cases $$I_{1} =0$$ and $$I_{1} \ne 0$$ using appropriate tools (bifurcation diagrams and the Lyapunov exponents, phase portraits, etc.). For both modes of operations, the system exhibits complex homogeneous and heterogeneous bifurcations, respectively marked by a large number of coexisting attractors. The roads to chaos unfold in the same scenario of period doubling. The Hamiltonian plot for the case $$I_{1} =0$$ allows us to observe an increase in the energy of the neuronal structure when it migrates from regular oscillations to irregular ones. Moreover, the existence of infinitely many coexisting homogeneous solutions (chaotic or periodic) is revealed for case $$I_{1} =0$$. In contrast, for $$I_{1} \ne 0$$ (i.e $$I_{1} =0.1)$$ the new model presents infinitely many coexisting hidden heterogeneous attractors (periodic and chaotic). An electronic circuit design of the new hyperbolic memristor enables the analog computer of the whole system to be designed for future engineering applications. Simulation results based on this analog computer in PSpice confirm those of the numerical investigations

Synchronization in a Multiplex Network of Nonidentical Fractional-Order Neurons

Fractional-order neuronal models that include memory effects can describe the rich dynamics of the firing of the neurons. This paper studies synchronization problems in a multiple network of Caputo–Fabrizio type fractional order neurons in which the orders of the derivatives in the layers are different. It is observed that the intralayer synchronization state occurs in weaker intralayer couplings when using nonidentical fractional-order derivatives rather than integer-order or identical fractional orders. Furthermore, the needed interlayer coupling strength for interlayer near synchronization decreases for lower fractional orders. The dynamics of the neurons in nonidentical layers are also considered. It is shown that in lower fractional orders, the neurons’ dynamics change to periodic when the near synchronization state occurs. Moreover, decreasing the derivative order leads to incrementing the frequency of the bursts in the synchronization manifold, which is in contrast to the behavior of the single neuron