Bifurcation analysis and control study of improved full-speed differential model in connected vehicle environment

In recent years, the traffic congestion problem has become more and more serious, and the research on traffic system control has become a new hot spot. Studying the bifurcation characteristics of traffic flow systems and designing control schemes for unstable pivots can alleviate the traffic congestion problem from a new perspective. In this work, the full-speed differential model considering the vehicle network environment is improved in order to adjust the traffic flow from the perspective of bifurcation control, the existence conditions of Hopf bifurcation and saddle-node bifurcation in the model are proved theoretically, and the stability mutation point for the stability of the transportation system is found. For the unstable bifurcation point, a nonlinear system feedback controller is designed by using Chebyshev polynomial approximation and stochastic feedback control method. The advancement, postponement, and elimination of Hopf bifurcation are achieved without changing the system equilibrium point, and the mutation behavior of the transportation system is controlled so as to alleviate the traffic congestion. The changes in the stability of complex traffic systems are explained through the bifurcation analysis, which can better capture the characteristics of the traffic flow. By adjusting the control parameters in the feedback controllers, the influence of the boundary conditions on the stability of the traffic system is adequately described, and the effects of the unstable focuses and saddle points on the system are suppressed to slow down the traffic flow. In addition, the unstable bifurcation points can be eliminated and the Hopf bifurcation can be controlled to advance, delay, and disappear,so as to realize the control of the stability behavior of the traffic system, which can help to alleviate the traffic congestion and describe the actual traffic phenomena as well.

Mechanism analysis of regulating Turing instability and Hopf bifurcation of malware propagation in mobile wireless sensor networks

A dynamical model is constructed to depict the spatial-temporal evolution of malware in mobile wireless sensor networks(MWSNs). Based on such a model, we design a hybrid control scheme combining parameter perturbation and state feedback to effectively manipulate the spatiotemporal dynamics of malware propagation. The hybrid control can not only suppress the Turing instability caused by diffusion factor but can also adjust the occurrence of Hopf bifurcation induced by time delay. Numerical simulation results show that the hybrid control strategy can efficiently manipulate the transmission dynamics to achieve our expected desired properties, thus reducing the harm of malware propagation to MWSNs.

Differences and Correlations of Morphological and Hemodynamic Parameters between Anterior Circulation Bifurcation and Side-wall Aneurysms

Objective:The objective of this research was to explore the difference and correlation of the morphological and hemodynamic features between sidewall and bifurcation aneurysms in anterior circulation arteries,utilizing computational fluid dynamics as a tool for analysis.Methods:In line with the designated inclusion criteria,this study covered 160 aneurysms identified in 131 patients who received treatment at Union Hospital of Tongji Medical College,Huazhong University of Science and Technology,China,from January 2021 to September 2022.Utilizing follow-up digital subtraction angiography(DSA)data,these cases were classified into two distinct groups:the sidewall aneurysm group and the bifurcation aneurysm group.Morphological and hemodynamic parameters in the immediate preoperative period were meticulously calculated and examined in both groups using a three-dimensional DSA reconstruction model.Results:No significant differences were found in the morphological or hemodynamic parameters of bifurcation aneurysms at varied locations within the anterior circulation.However,pronounced differences were identified between sidewall and bifurcation aneurysms in terms of morphological parameters such as the diameter of the parent vessel(Dvessel),inflow angle(θF),and size ratio(SR),as well as the hemodynamic parameter of inflow concentration index(ICI)(P<0.001).Notably,only the SR exhibited a significant correlation with multiple hemodynamic parameters(P<0.001),while the ICI was closely related to several morphological parameters(R>0.5,P<0.001).Conclusions:The significant differences in certain morphological and hemodynamic parameters between sidewall and bifurcation aneurysms emphasize the importance to contemplate variances in threshold values for these parameters when evaluating the risk of rupture in anterior circulation aneurysms.Whether it is a bifurcation or sidewall aneurysm,these disparities should be considered.The morphological parameter SR has the potential to be a valuable clinical tool for promptly distinguishing the distinct rupture risks associated with sidewall and bifurcation aneurysms.

Bifurcation Analysis of a Nonlinear Vibro-Impact System with an Uncertain Parameter via OPA Method

In this paper,the bifurcation properties of the vibro-impact systems with an uncertain parameter under the impulse and harmonic excitations are investigated.Firstly,by means of the orthogonal polynomial approximation(OPA)method,the nonlinear damping and stiffness are expanded into the linear combination of the state variable.The condition for the appearance of the vibro-impact phenomenon is to be transformed based on the calculation of themean value.Afterwards,the stochastic vibro-impact systemcan be turned into an equivalent high-dimensional deterministic non-smooth system.Two different Poincarésections are chosen to analyze the bifurcation properties and the impact numbers are identified for the periodic response.Consequently,the numerical results verify the effectiveness of the approximation method for analyzing the considered nonlinear system.Furthermore,the bifurcation properties of the system with an uncertain parameter are explored through the high-dimensional deterministic system.It can be found that the excitation frequency can induce period-doubling bifurcation and grazing bifurcation.Increasing the randomintensitymay result in a diffusion-based trajectory and the impact with the constraint plane,which induces the topological behavior of the non-smooth system to change drastically.It is also found that grazing bifurcation appears in advance with increasing of the random intensity.The stronger impulse force can result in the appearance of the diffusion phenomenon.

Logical stochastic resonance in a cross-bifurcation non-smooth system

This paper investigates logical stochastic resonance(LSR)in a cross-bifurcation non-smooth system driven by Gaussian colored noise.In this system,a bifurcation parameter triggers a transition between monostability,bistability and tristability.By using Novikov's theorem and the unified colored noise approximation method,the approximate Fokker-Planck equation is obtained.Then we derive the generalized potential function and the transition rates to analyze the LSR phenomenon using numerical simulations.We simulate the logic operation of the system in the bistable and tristable regions respectively.We assess the impact of Gaussian colored noise on the LSR and discover that the reliability of the logic response depends on the noise strength and the bifurcation parameter.Furthermore,it is found that the bistable region has a more extensive parameter range to produce reliable logic operation compared with the tristable region,since the tristable region is more sensitive to noise than the bistable one.

Research on the Stability Analysis Method of DC Microgrid Based on Bifurcation and Strobe Theory

During the operation of a DC microgrid,the nonlinearity and low damping characteristics of the DC bus make it prone to oscillatory instability.In this paper,we first establish a discrete nonlinear system dynamic model of a DC microgrid,study the effects of the converter sag coefficient,input voltage,and load resistance on the microgrid stability,and reveal the oscillation mechanism of a DC microgrid caused by a single source.Then,a DC microgrid stability analysis method based on the combination of bifurcation and strobe is used to analyze how the aforementioned parameters influence the oscillation characteristics of the system.Finally,the stability region of the system is obtained by the Jacobi matrix eigenvalue method.Grid simulation verifies the feasibility and effectiveness of the proposed method.

Bifurcation Analysis Reveals Solution Structures of Phase Field Models

The phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems.Here,we develop a new analytical approach based on the bifurcation analysis to explore the mathematical solution structure of phase field models.Revealing such solution structures not only is of great mathematical interest but also may provide guidance to experimentally or computationally uncover new morphological evolution phenomena in materials undergoing electronic and structural phase transitions.To elucidate the idea,we apply this analytical approach to three representative phase field equations:the Allen-Cahn equation,the Cahn-Hilliard equation,and the Allen-Cahn-Ohta-Kawasaki system.The solution structures of these three phase field equations are also verified numerically by the homotopy continuation method.

Finite Deformation, Finite Strain Nonlinear Dynamics and Dynamic Bifurcation in TVE Solids with Rheology

This paper presents a mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and ordered rate constitutive theories in Lagrangian description derived using entropy inequality and the representation theorem for thermoviscoelastic solids (TVES) with rheology. The CBL and the constitutive theories take into account finite deformation and finite strain deformation physics and are based on contravariant deviatoric second Piola-Kirchhoff stress tensor and its work conjugate covariant Green’s strain tensor and their material derivatives of up to order m and n respectively. All published works on nonlinear dynamics of TVES with rheology are mostly based on phenomenological mathematical models. In rare instances, some aspects of CBL are used but are incorrectly altered to obtain mass, stiffness and damping matrices using space-time decoupled approaches. In the work presented in this paper, we show that this is not possible using CBL of CCM for TVES with rheology. Thus, the mathematical models used currently in the published works are not the correct description of the physics of nonlinear dynamics of TVES with rheology. The mathematical model used in the present work is strictly based on the CBL of CCM and is thermodynamically and mathematically consistent and the space-time coupled finite element methodology used in this work is unconditionally stable and provides solutions with desired accuracy and is ideally suited for nonlinear dynamics of TVES with memory. The work in this paper is the first presentation of a mathematical model strictly based on CBL of CCM and the solution of the mathematical model is obtained using unconditionally stable space-time coupled computational methodology that provides control over the errors in the evolution. Both space-time coupled and space-time decoupled finite element formulations are considered for obtaining solutions of the IVPs described by the mathematical model and are presented in the paper. Factors or the physics influencing dynamic response and dynamic bifurcation for TVES with rheology are identified and are also demonstrated through model problem studies. A simple model problem consisting of a rod (1D) of TVES material with memory fixed at one end and subjected to harmonic excitation at the other end is considered to study nonlinear dynamics of TVES with rheology, frequency response as well as dynamic bifurcation phenomenon.

Two-Stent Strategy for Bifurcation Lesions in Percutaneous Transluminal Coronary Angioplasty: Real-World Evidence

Background: Bifurcation lesions pose a high risk for adverse events after percutaneous coronary intervention (PCI). Evidence supporting the benefits of the two-stent strategy (2SS) for treating coronary bifurcation lesions in India is limited. This study aimed to evaluate the clinical outcomes of various 2SSs for percutaneous transluminal coronary angioplasty for bifurcation lesions in India. Materials and Methods: This retrospective, observational, multicentric, real-world study included 64 patients over 8 years. Data on demographics, medical history, PCI procedures, and outcomes were recorded. Descriptive statistics were computed using the SPSS software. Results: Patients (n = 64) had an average age of 65.3 ± 11.1 years, with 78.1% males. Acute coronary syndrome was reported in 18.8%, chronic stable angina in 40.6%, and unstable angina in 34.4% of participants. Two-vessel disease was observed in 98.4% of patients, and 99.4% had true bifurcation lesions. The commonly involved vessels were the left anterior descending artery (50%), left circumflex coronary artery (34.4%), and first diagonal artery (43.8%). Mean percent diameter stenosis was 87.2% ± 10.1%. The mean number of stents used was 2.00 ± 0.34. The 2SS techniques included the T and small protrusion (TAP) (39.1%), double kissing (DK) crush (18.8%), and the culotte techniques (14.1%). Procedural and angiographic success rate was 92.18%. Major adverse cardiovascular events at 1-year follow-up occurred in 7.8% of cases. Conclusion: The 2SS for bifurcation lesions showed favorable in-hospital and follow-up outcomes. Findings can serve as a resource for bifurcation angioplasty in India. Larger real-world studies with robust methodology are needed to validate these results.

Bifurcations, Analytical and Non-Analytical Traveling Wave Solutions of (2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation

For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.

Bifurcation and Turing Pattern Formation in a Diffusion Modified Leslie-Gower Predator-Prey Model with Crowley-Martin Functional Response

In this paper, we study a modified Leslie-Gower predator-prey model with Smith growth subject to homogeneous Neumann boundary condition, in which the functional response is the Crowley-Martin functional response term. Firstly, for ODE model, the local stability of equilibrium point is given. And by using bifurcation theory and selecting suitable bifurcation parameters, we find many kinds of bifurcation phenomena, including Transcritical bifurcation and Hopf bifurcation. For the reaction-diffusion model, we find that Turing instability occurs. Besides, it is proved that Hopf bifurcation exists in the model. Finally, numerical simulations are presented to verify and illustrate the theoretical results.

Stochastic Bifurcation of an SIS Epidemic Model with Treatment and Immigration

In this paper, we investigate an SIS model with treatment and immigration. Firstly, the two-dimensional model is simplified by using the stochastic averaging method. Then, we derive the local stability of the stochastic system by computing the Lyapunov exponent of the linearized system. Further, the global stability of the stochastic model is analyzed based on the singular boundary theory. Moreover, we prove that the model undergoes a Hopf bifurcation and a pitchfork bifurcation. Finally, several numerical examples are provided to illustrate the theoretical results. .

Generalized Hopf Bifurcation in a Delay Model of Neutrophil Cells Model

The DDE-Biftool software is applied to solve the dynamical stability and bifurcation problem of the neutrophil cells model. Based on Hopf point finding with the stability property of the equilibrium solution loss, the continuation of the bifurcating periodical solution starting from Hopf point is exploited. The generalized Hopf point is tracked by seeking for the critical value of free parameter of the switching phenomena of the open loop, which describes the lineup of bifurcating periodical solutions from Hopf point. The normal form near the generalized Hopf point is computed by Lyapunov-Schimdt reduction scheme combined with the center manifold analytical technique. The near dynamics is classified by geometrically different topological phase portraits.

Thermomechanical Dynamics (TMD) and Bifurcation-Integration Solutions in Nonlinear Differential Equations with Time-Dependent Coefficients

The new independent solutions of the nonlinear differential equation with time-dependent coefficients (NDE-TC) are discussed, for the first time, by employing experimental device called a drinking bird whose simple back-and-forth motion develops into water drinking motion. The solution to a drinking bird equation of motion manifests itself the transition from thermodynamic equilibrium to nonequilibrium irreversible states. The independent solution signifying a nonequilibrium thermal state seems to be constructed as if two independent bifurcation solutions are synthesized, and so, the solution is tentatively termed as the bifurcation-integration solution. The bifurcation-integration solution expresses the transition from mechanical and thermodynamic equilibrium to a nonequilibrium irreversible state, which is explicitly shown by the nonlinear differential equation with time-dependent coefficients (NDE-TC). The analysis established a new theoretical approach to nonequilibrium irreversible states, thermomechanical dynamics (TMD). The TMD method enables one to obtain thermodynamically consistent and time-dependent progresses of thermodynamic quantities, by employing the bifurcation-integration solutions of NDE-TC. We hope that the basic properties of bifurcation-integration solutions will be studied and investigated further in mathematics, physics, chemistry and nonlinear sciences in general.

Effects of viscoelasticity on the stability and bifurcations of nonlinear energy sinks

Due to the increasing use of passive absorbers to control unwanted vibrations,many studies have been done on energy absorbers ideally,but the lack of studies of real environmental conditions on these absorbers is felt.The present work investigates the effect of viscoelasticity on the stability and bifurcations of a system attached to a nonlinear energy sink(NES).In this paper,the Burgers model is assumed for the viscoelasticity in an NES,and a linear oscillator system is considered for investigating the instabilities and bifurcations.The equations of motion of the coupled system are solved by using the harmonic balance and pseudo-arc-length continuation methods.The results show that the viscoelasticity affects the frequency intervals of the Hopf and saddle-node branches,and by increasing the stiffness parameters of the viscoelasticity,the conditions of these branches occur in larger ranges of the external force amplitudes,and also reduce the frequency range of the branches.In addition,increasing the viscoelastic damping parameter has the potential to completely eliminate the instability of the system and gradually reduce the amplitude of the jump phenomenon.

BIFURCATION ANALYSIS IN A PREDATOR-PREY MODEL WITH AN ALLEE EFFECT AND A DELAYED MECHANISM

Regarding delay-induced predator-prey models, much research has been done on delayed destabilization, but whether delays are stabilizing or destabilizing is a subtle issue. In this study, we investigate predator-prey dynamics affected by both delays and the Allee effect. We analyze the consequences of delays in different feedback mechanisms. The existence of a Hopf bifurcation is studied, and we calculate the value of the delay that leads to the Hopf bifurcation. Furthermore, applying the normal form theory and a center manifold theorem, we consider the direction and stability of the Hopf bifurcation. Finally, we present numerical experiments that validate our theoretical analysis. Interestingly, depending on the chosen delay mechanism, we find that delays are not necessarily destabilizing. The Allee effect generally increases the stability of the equilibrium, and when the Allee effect involves a delay term, the stabilization effect is more pronounced.

Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh–Rose and FitzHugh–Nagumo neurons with two time delays

A memristor-coupled heterogenous neural network consisting of two-dimensional(2D)FitzHugh–Nagumo(FHN)and Hindmarsh–Rose(HR)neurons with two time delays is established.Taking the time delays as the control parameters,the existence of Hopf bifurcation near the stable equilibrium point in four cases is derived theoretically,and the validity of the Hopf bifurcation condition is verified by numerical analysis.The results show that the two time delays can make the stable equilibrium point unstable,thus leading to periodic oscillations induced by Hopf bifurcation.Furthermore,the time delays in FHN and HR neurons have different effects on the firing activity of neural network.Complex firing patterns,such as quiescent state,chaotic spiking,and periodic spiking can be induced by the time delay in FHN neuron,while the neural network only exhibits quiescent state and periodic spiking with the change of the time delay in HR neuron.Especially,phase synchronization between the heterogeneous neurons is explored,and the results show that the time delay in HR neurons has a greater effect on blocking the synchronization than the time delay in FHN neuron.Finally,the theoretical analysis is verified by circuit simulations.

Research on hunting stability and bifurcation characteristics of nonlinear stochastic wheelset system

A stochastic wheelset model with a nonlinear wheel-rail contact relationship is established to investigate the stochastic stability and stochastic bifurcation of the wheelset system with the consideration of the stochastic parametric excitations of equivalent conicity and suspension stiffness.The wheelset is systematized into a onedimensional(1D)diffusion process by using the stochastic average method,the behavior of the singular boundary is analyzed to determine the hunting stability condition of the wheelset system,and the critical speed of stochastic bifurcation is obtained.The stationary probability density and joint probability density are derived theoretically.Based on the topological structure change of the probability density function,the stochastic Hopf bifurcation form and bifurcation condition of the wheelset system are determined.The effects of stochastic factors on the hunting stability and bifurcation characteristics are analyzed,and the simulation results verify the correctness of the theoretical analysis.The results reveal that the boundary behavior of the diffusion process determines the hunting stability of the stochastic wheelset system,and the left boundary characteristic value cL=1 is the critical state of hunting stability.Besides,stochastic D-bifurcation and P-bifurcation will appear in the wheelset system,and the critical speeds of the two kinds of stochastic bifurcation decrease with the increase in the stochastic parametric excitation intensity.

BIFURCATION CONTROL FOR A FRACTIONAL-ORDER DELAYED SEIR RUMOR SPREADING MODEL WITH INCOMMENSURATE ORDERS

A fractional-order delayed SEIR rumor spreading model with a nonlinear incidence function is established in this paper,and a novel strategy to control the bifurcation of this model is proposed.First,Hopf bifurcation is investigated by considering time delay as bifurcation parameter for the system without a feedback controller.Then,a state feedback controller is designed to control the occurrence of bifurcation in advance or to delay it by changing the parameters of the controller.Finally,in order to verify the theoretical results,some numerical simulations are given.

Current bifurcation, reversals and multiple mobility transitions of dipole in alternating electric fields

Anomalous transports of dipole in alternating electric fields are investigated by means of numerical calculation of its average angular velocity(or current). Our results show that the alternating electric fields can make the dipole exhibit many interesting transport behaviors. There exist current bifurcation and multiple current reversal phenomena about frequency of the alternating electric fields in the system in the absence of constant bias force, while many platforms appear in the curve of its average angular velocity vs. the force, i.e., multiple mobility transitions phenomenon in the presence of the constant force, dependent on frequencies of the alternating electric fields. Further investigation indicates that the multiple mobility transitions are attributed to the traveling forces on the dipole. Intrinsic physical mechanism and conditions for the characteristic dynamical behaviors to occur are also discussed in detail. These findings will possess crucial significance for optimizing heating control in the alternating electric fields.