Exploring nonlinearity in quarter car models with an experimental approach to formulating fractional order form and its dynamic analysis.

This study explores the inherent nonlinearity of quarter car models by employing an experimental and numerical approach. The dynamics of vehicular suspension systems are pivotal for ensuring passenger comfort, vehicle stability, and overall ride quality. In this paper we assessed the impact of various parameters and components on suspension performance, enabled the optimization of ride comfort, stability, and handling characteristics. Firstly, experimental analysis allowed for the investigation of factors that are challenging to model theoretically, such as stiffness nonlinearity and damping characteristics, which may vary under different operating conditions. Time domain and frequency response diagram of the model has been obtained. Secondly, a quarter-car with single degree-of-freedom presented and investigated in fractional order form. Fractional order dynamics emphasize nonlinearities in quarter car models, capturing real-world dynamics effectively. The proposed fractional-order nonlinear quarter car model employed Caputo derivative. For numerical analysis of fractional order system, the Adam-Bashforth-Moulton method is used and the disturbance of road assumed to be stochastic. Results show that the dynamic response of the vehicle can be chaotic. Influence of road roughness amplitude and frequency on vehicle vibration is investigated.

Dynamics, synchronization and traveling wave patterns of flux coupled network of Chay neurons.

Studies in the literature have demonstrated the significance of the synchronization of neuronal electrical activity for signal transmission and information encoding. In light of this importance, we investigate the synchronization of the Chay neuron model using both theoretical analysis and numerical simulations. The Chay model is chosen for its comprehensive understanding of neuronal behavior and computational efficiency. Additionally, we explore the impact of electromagnetic induction, leading to the magnetic flux Chay neuron model. The single neuron model exhibits rich and complex dynamics for various parameter choices. We explore the bifurcation structure of the model through bifurcation diagrams and Lyapunov exponents. Subsequently, we extend our study to two coupled magnetic flux Chay neurons, identifying mode locking and structures reminiscent of Arnold's tongue. We evaluate the stability of the synchronized manifold using Lyapunov theory and confirm our findings through simulations. Expanding our study to networks of diffusively coupled flux Chay neurons, we observe coherent, incoherent, and imperfect chimera patterns. Our investigation of three network types highlights the impact of network topology on the emergent dynamics of the Chay neuron network. Regular networks exhibit diverse patterns, small-world networks demonstrate a critical transition to coherence, and random networks showcase synchronization at specific coupling strengths. These findings significantly contribute to our understanding of the synchronization patterns exhibited by the magnetic flux Chay neuron. To assess the synchronization stability of the Chay neuron network, we employ master stability function analysis.

Effect of the electromagnetic induction on a modified memristive neural map model.

The significance of discrete neural models lies in their mathematical simplicity and computational ease. This research focuses on enhancing a neural map model by incorporating a hyperbolic tangent-based memristor. The study extensively explores the impact of magnetic induction strength on the model's dynamics, analyzing bifurcation diagrams and the presence of multistability. Moreover, the investigation extends to the collective behavior of coupled memristive neural maps with electrical, chemical, and magnetic connections. The synchronization of these coupled memristive maps is examined, revealing that chemical coupling exhibits a broader synchronization area. Additionally, diverse chimera states and cluster synchronized states are identified and discussed.

Synchronization Studies of Hindmarsh-Rose Neuron Networks: Unraveling the Influence of connection induced memristive synapse.

This study focuses on the synchronization analysis of Hindmarsh-Rose neurons coupled through a common memristor (coupled mHRN). Initially, we thoroughly examine the synchronization of two mHRNs coupled via a common memristor before exploring synchronization in a network of mHRNs. The stability of the proposed model is analyzed in three cases, demonstrating the existence of a single equilibrium point whose stability is influenced by external stimuli. The stable and unstable regions are investigated using eigenvalues. Through bifurcation analysis and the determination of maximum Lyapunov exponents, we identify chaotic and hyperchaotic trajectories. Additionally, using the next-generation matrix method, we calculate the chaotic number C0, demonstrating the influence of coupling strength on the chaotic and hyperchaotic behavior of the system. The exponential stability of the synchronous mHRN is derived analytically using Lyapunov theory, and our results are verified through numerical simulations. Furthermore, we explore the impact of initial conditions and memristor synapses, as well as the coupling coefficient, on the synchronization of coupled mHRN. Finally, we investigate a network consisting of n number of mHRNs and observe various collective behaviors, including incoherent, coherent, traveling patterns, traveling wave chimeras, and imperfect chimeras, which are determined by the memristor coupling coefficient.

The Intricacies of Sprott-B System with Fractional-Order Derivatives: Dynamical Analysis, Synchronization, and Circuit Implementation.

Studying simple chaotic systems with fractional-order derivatives improves modeling accuracy, increases complexity, and enhances control capabilities and robustness against noise. This paper investigates the dynamics of the simple Sprott-B chaotic system using fractional-order derivatives. This study involves a comprehensive dynamical analysis conducted through bifurcation diagrams, revealing the presence of coexisting attractors. Additionally, the synchronization behavior of the system is examined for various derivative orders. Finally, the integer-order and fractional-order electronic circuits are implemented to validate the theoretical findings. This research contributes to a deeper understanding of the Sprott-B system and its fractional-order dynamics, with potential applications in diverse fields such as chaos-based secure communications and nonlinear control systems.

Collective dynamics of a coupled Hindmarsh-Rose neurons with locally active memristor.

A Locally active memristors can mimic neural synapses, resulting in rich neuro-morphological dynamics in biological neurons. To illustrate the impact of a local active memristive synapse, we consider coupled Hindmarsh-Rose (HR) neurons. Firstly, the dynamical transitions of the proposed system are investigated using bifurcation analysis and Lyapunov exponents, and we find that the transition between periodic and chaotic states depends on the input currents and memristive coupling strength. By performing the two-parameter analysis, the existence of periodic and chaotic regions is revealed. The collective behavior is then examined by expanding the network to include memristive coupled HR neurons under different network connectivities. We show that the system achieves synchronization behavior for all network connectivities, including regular, random, and small-world, when the strength of the memristive coupling is increased.

Energy computation and multiplier-less implementation of the two-dimensional FitzHugh-Nagumo (FHN) neural circuit.

In this work, with the aim of reducing the cost of the implementation of the traditional 2D FHN neuron circuit, a pair of diodes connected in an anti-parallel direction is used to replace the usual cubic nonlinearity (implemented with two multipliers). Based on the stability of the model, the generation of self-excited firing patterns is justified. Making use of the famous Helmholtz theorem, a Hamilton function is provided for the estimation of the energy released during each electrical activity of the model. From the investigation of the 1D evolution of the maxima of the membrane potential of the model, it was recorded that the considered model is able to experience a period of doubling bifurcation followed by a crisis that enables the increasing of the volume of the attractor. This contribution ends with the realization of a neural circuit without analog multipliers for the validation of the obtained results.

Impact of external excitations on blinking enhanced synchronization in bistable vibrational energy harvesters.

Vibrational energy harvesters are capable of converting low-frequency broad-band mechanical energy into electrical power and can be used in implantable medical devices and wireless sensors. With the use of such energy harvesters, it is feasible to generate continuous power that is more reliable and cost-effective. According to previous findings, the energy harvester can offer rich complex dynamics, one of which is obtaining the synchronization behavior, which is intriguing to achieve desirable power from energy harvesters. Therefore, we consider bistable energy harvesters with periodic and quasiperiodic excitations to investigate synchronization. Specifically, we introduce blinking into the coupling function to check whether it improves the synchronization. Interestingly, we discover that raising the normalized proportion of blinking can initiate synchronization behaviors even with lower optimal coupling strength than the absence of blinking in the coupling (i.e., continuous coupling). The existence of synchronization behaviors is confirmed by finding the largest Lyapunov exponents. In addition, the results show that the optimal coupling strength needed to achieve synchronization for quasiperiodic excitations is smaller than that for periodic excitations.

Investigation of an improved FitzHugh-Rinzel neuron and its multiplier-less circuit implementation.

Circuit implementation of the mathematical model of neurons represents an alternative approach for the validation of their dynamical behaviors for their potential applications in neuromorphic engineering. In this work, an improved FitzHugh-Rinzel neuron, in which the traditional cubic nonlinearity is swapped with a sine hyperbolic function, is introduced. This model has the advantage that it is multiplier-less since the nonlinear component is just implemented with two diodes in anti-parallel. The stability of the proposed model revealed that it has both stable and unstable nodes around its fixed points. Based on the Helmholtz theorem, a Hamilton function that enables the estimation of the energy released during the various modes of electrical activity is derived. Furthermore, numerical computation of the dynamic behavior of the model revealed that it was able to experience coherent and incoherent states involving both bursting and spiking. In addition, the simultaneous appearance of two different types of electric activity for the same neuron parameters is also recorded by just varying the initial states of the proposed model. Finally, the obtained results are validated using the designed electronic neural circuit, which has been analyzed in the Pspice simulation environment.

Complex dynamics in a fractional order nephron pressure and flow regulation model.

Cardiovascular diseases can be attributed to irregular blood pressure, which may be caused by malfunctioning kidneys that regulate blood pressure. Research has identified complex oscillations in the mechanisms used by the kidney to regulate blood pressure. This study uses established physiological knowledge and earlier autoregulation models to derive a fractional order nephron autoregulation model. The dynamical behaviour of the model is analyzed using bifurcation plots, revealing periodic oscillations, chaotic regions, and multistability. A lattice array of the model is used to study collective behaviour and demonstrates the presence of chimeras in the network. A ring network of the fractional order model is also considered, and a diffusion coupling strength is adopted. A basin of synchronization is derived, considering coupling strength, fractional order or number of neighbours as parameters, and measuring the strength of incoherence. Overall, the study provides valuable insights into the complex dynamics of the nephron autoregulation model and its potential implications for cardiovascular diseases.

Obstacle induced spiral waves in a multilayered Huber-Braun (HB) neuron model.

Various dynamical properties of four-dimensional mammalian cold receptor model have been discussed widely in the literature considering noise and temperature as important parameters of discussion. Though various spiking and bursting behaviors of the neuron under various noise and temperature conditions studied for a single neuron, no much discussions have been done on the collective behavior. We investigate the collective behavior of these temperature dependent stochastic neurons and unlike the neuron models when forced by periodic external force there is no wave reentry or spiral waves in the network. Hence, we introduce obstacle in the network and depending on the orientation and size of the introduced obstacle, we could show their effects on the wave reentry in the network. Various significant discussions are produced in this paper to confirm that obstacles placed parallel to the wave entry affects the excitability of the tissues significantly compared to those obstacles place perpendicular. We could also show that those obstacles which are lesser in dimensions doesn't affect the excitabilities and hence doesn't contribute for wave reentry. We introduce a new technique to identify wave reentry and spiral waves using the period of individual nodes is proposed. This technique could help us identify even the lowest of excitability change which cannot be seen when using spatiotemporal snapshots.

A discrete Huber-Braun neuron model: from nodal properties to network performance.

Many of the well-known neuron models are continuous time systems with complex mathematical definitions. Literatures have shown that a discrete mathematical model can effectively replicate the complete dynamical behaviour of a neuron with much reduced complexity. Hence, we propose a new discrete neuron model derived from the Huber-Braun neuron with two additional slow and subthreshold currents alongside the ion channel currents. We have also introduced temperature dependent ion channels to study its effects on the firing pattern of the neuron. With bifurcation and Lyapunov exponents we showed the chaotic and periodic regions of the discrete model. Further to study the complexity of the neuron model, we have used the sample entropy algorithm. Though the individual neuron analysis gives us an idea about the dynamical properties, it's the collective behaviour which decides the overall behavioural pattern of the neuron. Hence, we investigate the spatiotemporal behaviour of the discrete neuron model in single- and two-layer network. We have considered obstacle as an important factor which changes the excitability of the neurons in the network. Literatures have shown that spiral waves can play a positive role in breaking through quiescent areas of the brain as a pacemaker by creating a coherence resonance behaviour. Hence, we are interested in studying the induced spiral waves in the network. In this condition when an obstacle is introduced the wave propagation is disturbed and we could see multiple wave re-entry and spiral waves. In a two-layer network when the obstacle is considered only in one layer and stimulus applied to the layer having the obstacle, the wave re-entry is seen in both the layer though the other layer is not exposed to obstacle. But when both the layers are inserted with an obstacle and stimuli also applied to the layers, they behave like independent layers with no coupling effect. In a two-layer network, stimulus play an important role in spatiotemporal dynamics of the network. Supplementary Information: The online version contains supplementary material available at 10.1007/s11571-022-09806-1.

Spiral waves in a hybrid discrete excitable media with electromagnetic flux coupling.

Though there are many neuron models based on differential equations, the complexity in realizing them into digital circuits is still a challenge. Hence, many new discrete neuron models have been recently proposed, which can be easily implemented in digital circuits. We consider the well-known FitzHugh-Nagumo model and derive the discrete version of the model considering the sigmoid type of recovery variable and electromagnetic flux coupling. We show the various time series plots confirming the existence of periodic and chaotic bursting as in differential equation type neuron models. Also, we have used the bifurcation plots, Lyapunov exponents, and frequency bifurcations to investigate the dynamics of the proposed discrete neuron model. Different topologies of networks like single, two, and three layers are considered to analyze the wave propagation phenomenon in the network. We introduce the concept of using energy levels of nodes to study the spiral wave existence and compare them with the spatiotemporal snapshots. Interestingly, the energy plots clearly show that when the energy level of nodes is different and distributed, the occurrence of the spiral waves is identified in the network.

Effect of magnetic induction on the synchronizability of coupled neuron network.

Master stability functions (MSFs) are significant tools to identify the synchronizability of nonlinear dynamical systems. For a network of coupled oscillators to be synchronized, the corresponding MSF should be negative. The study of MSF will normally be discussed considering the coupling factor as a control variable. In our study, we considered various neuron models with electromagnetic flux induction and investigated the MSF's zero-crossing points for various values of the flux coupling coefficient. Our numerical analysis has shown that in all the neuron models we considered, flux coupling has increased the synchronization of the coupled neuron by increasing the number of zero-crossing points of MSFs or by achieving a zero-crossing point for a lesser value of a coupling parameter.

Noise induced suppression of spiral waves in a hybrid FitzHugh-Nagumo neuron with discontinuous resetting.

A modified FitzHugh-Nagumo neuron model with sigmoid function-based recovery variable is considered with electromagnetic flux coupling. The dynamical properties of the proposed neuron model are investigated, and as the excitation current becomes larger, the number of fixed points decreases to one. The bifurcation plots are investigated to show the chaotic and periodic regimes for various values of excitation current and parameters. A N×N network of the neuron model is constructed to study the wave propagation and wave re-entry phenomena. Investigations are conducted to show that for larger flux coupling values, the spiral waves are suppressed, but for such values of the flux coupling, the individual nodes are driven into periodic regimes. By introducing Gaussian noise as an additional current term, we showed that when noise is introduced for the entire simulation time, the dynamics of the nodes are largely altered while the noise exposure for 200-time units will not alter the dynamics of the nodes completely.

Size matters: Effects of the size of heterogeneity on the wave re-entry and spiral wave formation in an excitable media.

Network performance of neurons plays a vital role in determining the behavior of many physiological systems. In this paper, we discuss the wave propagation phenomenon in a network of neurons considering obstacles in the network. Numerous studies have shown the disastrous effects caused by the heterogeneity induced by the obstacles, but these studies have been mainly discussing the orientation effects. Hence, we are interested in investigating the effects of both the size and orientation of the obstacles in the wave re-entry and spiral wave formation in the network. For this analysis, we have considered two types of neuron models and a pancreatic beta cell model. In the first neuron model, we use the well-known differential equation-based neuron models, and in the second type, we used the hybrid neuron models with the resetting phenomenon. We have shown that the size of the obstacle decides the spiral wave formation in the network and horizontally placed obstacles will have a lesser impact on the wave re-entry than the vertically placed obstacles.

Local and network behavior of bistable vibrational energy harvesters considering periodic and quasiperiodic excitations.

Vibrational energy harvesters can exhibit complex nonlinear behavior when exposed to external excitations. Depending on the number of stable equilibriums, the energy harvesters are defined and analyzed. In this work, we focus on the bistable energy harvester with two energy wells. Though there have been earlier discussions on such harvesters, all these works focus on periodic excitations. Hence, we are focusing our analysis on both periodic and quasiperiodic forced bistable energy harvesters. Various dynamical properties are explored, and the bifurcation plots of the periodically excited harvester show coexisting hidden attractors. To investigate the collective behavior of the harvesters, we mathematically constructed a two-dimensional lattice array of the harvesters. A non-local coupling is considered, and we could show the emergence of chimeras in the network. As discussed in the literature, energy harvesters are efficient if the chaotic regimes can be suppressed and hence we focus our discussion toward synchronizing the nodes in the network when they are not in their chaotic regimes. We could successfully define the conditions to achieve complete synchronization in both periodic and quasiperiodically excited harvesters.

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

The last two decades have seen many literatures on the mathematical and computational analysis of neuronal activities resulting in many mathematical models to describe neuron. Many of those models have described the membrane potential of a neuron in terms of the leakage current and the synaptic inputs. Only recently researchers have proposed a new neuron model based on the electromagnetic induction theorem, which considers inner magnetic fluctuation and external electromagnetic radiation as a significant missing part that can participate in neural activity. While the flux coupling of the membrane is considered equivalent to a memductance function of a memristor, standard memductance model of α + 3 ß Ï• 2 has been used in the literatures, but in this paper we propose a new memductance function based on discontinuous flux coupling. Various dynamical properties of the neuron model with discontinuous flux coupling are studied and interestingly the proposed model shows hyperchaotic behavior which was not identified in the literatures. Furthermore, we consider a ring network of the proposed model and investigate whether the chimera state can emerge. The chimera state relates to the state with simultaneously coherence and incoherence in oscillatory networks and has received much attention in recent years.

Improving the Diagnosis of Scrub Typhus by Combining groEL Based Polymerase Chain Reaction and IgM ELISA.

INTRODUCTION: Scrub typhus, an acute febrile illness, caused by Orientia tsutsugamushi, is an important cause of pyrexia of unknown origin in regions of endemicity. This disease is mostly underdiagnosed or misdiagnosed, the reasons for this being a combination of factors which include clinical manifestations that can mimic other infections, lack of easy and reliable diagnostic methods and variation among strains in endemic areas. Hence, easy and reliable methods of diagnosis will contribute to rapid identification and treatment of the infection. AIM: The aim of the study was to compare four different methods of detection of scrub typhus and to identify one single test or a combination of tests detecting maximum number of cases. MATERIALS AND METHODS: One hundred and forty-five suspected scrub typhus cases were included in this study. Duration of fever and presence of eschar in each patient was noted down. Enzyme-Linked Immunosorbent Assay (ELISA) to detect Immunoglobulin M (IgM) antibodies and Polymerase Chain Reaction (PCR) to detect three genes of Orientia, namely, 56 kDa, 16S rRNA, and groEL were done on these samples. The results of each test were analyzed to identify the test picking up maximum number of positive samples. Statistical analysis was performed using Chi-square test. The level of significance was set at p<0.05. RESULTS: These tests showed that IgM ELISA (93%) and PCR (68%) picked up maximum number of positives. Statistical analysis performed using Chi-square test between the diagnostic assays showed that the p - value <0.001 was significant for IgM ELISA. Among the molecular markers, p-value was significant (<0.001) for groEL PCR. Further analysis of eschar positivity and duration of fever also showed that groEL PCR could detect DNA of the bacterium even in cases with 10 days of fever and this PCR was the best among the molecular markers used to detect the infection. CONCLUSION: This study suggests that IgM detection by ELISA and conventional groEL PCR, either in combination or alone, depending on the duration of fever, would enhance the diagnosis of scrub typhus.