Modelling the effects of heavy alcohol consumption on the transmission dynamics of gonorrhea

Prior studies have indicated that heavy alcohol drinkers are likely to engage in risky sexual behaviours and thus, more likely to get sexually transmitted infections (STIs) than social drinkers. Here, we formulate a deterministic model for evaluating the impact of heavy alcohol drinking on the reemerging gonorrhea epidemic. The model is rigorously analysed, showing the existence of a globally asymptotically stable disease-free equilibrium whenever the reproductive number is less than unity. If the disease threshold number is greater than unity, a unique endemic equilibrium exists and is globally asymptotically stable in the interior of the feasible region and the disease persists at endemic proportions if it is initially present. Both analytical and numerical results are provided to ascertain whether heavy alcohol drinking has an impact on the transmission dynamics of gonorrhea.     

The influences of both offset and mass moment of inertia of a tip mass on the dynamics of a centrifugally stiffened visco-elastic beam

The present study is concerned with the out-of-plane vibrations of a rotating, internally damped (Kelvin-Voigt model) Bernoulli-Euler beam carrying a tip mass. The centroid of the tip mass, possessing also a mass moment of inertia is offset from the free end of the beam and is located along its extended axis. This system can be thought of as an extremely simplified model of a helicopter rotor blade or a blade of an auto-cooling fan. The differential eigenvalue problem is solved by using Frobenius method of solution in power series. The characteristic equation is then solved numerically. The simulation results are tabulated for a variety of the nondimensional rotational speeds, tip mass, tip mass offset, mass moment of inertia and internal damping parameters. These are compared with the results of a conventional finite element modeling as well, and excellent agreement is obtained. Some numerical results are given in graphical form. The numerical results obtained, indicate clearly that the tip mass offset and mass moment of inertia are important parameters on the eigencharacteristics of rotating beams so that they have to be included in the modeling process.     

Nonlinear dynamics of a delayed Leslie predator–prey model

The present paper is concerned with a delayed Leslie predator–prey model. The conditions of boundedness of the solutions of the system, existence, and stability of the equilibrium of the system are investigated. Meanwhile, we find that the system can also undergo a Hopf bifurcation of nonconstant periodic solution at the positive equilibrium when the delay crosses through a sequence of critical values. The extensive simulations carried out show that the bifurcations arise around the positive equilibrium.     

Optimal control of the transmission dynamics of tuberculosis

This paper deals with the problem of optimal control for the transmission dynamics of tuberculosis (TB). A tuberculosis model which incorporates the essential biological and epidemiological features of the disease such as exogenous reinfection and chemoprophylaxis of latently infected individuals, and treatment of the infectious is developed and rigorously analyzed. Based on this continuous model, the tuberculosis control is formulated and solved as an optimal control theory problem, indicating how a control term on the chemoprophylaxis should be introduced in the population to reduce the number of individuals with active TB. The feedback control law has been proved to be capable of reducing the number of individuals with active TB. An advantage is that the proposed scheme accounts for the energy wasted by the controller and the closed-loop performance on tracking. Numerical results show the performance of the optimization strategy.     

Investigation on effect of joint clearance on dynamics of four-bar mechanism

As a result of design, manufacturing and assembly processes or a wear effect, clearances are inevitable at the joints of mechanisms. In this study, dynamic response of mechanism having revolute joints with clearance is investigated. A four-bar mechanism having two joints with clearance is considered as a model mechanism. A neural network was used to model several characteristics of joint clearance. Kinematic and dynamic analyses were achieved using continuous contact mode between journal and bearing. A genetic algorithm was also used to determine the appropriate values of design variables for reducing the additional vibration effect due primarily to the joint clearance. The results show that the optimal adjusting of suitable design variables gives a certain decrease in shaking forces and their moments on the mechanism frame.     

Control problems of a mathematical model for schistosomiasis transmission dynamics

Drug treatment, snail control, cercariae control, improved sanitation and health education are the effective strategies which are used to control the schistosomiasis. In this paper, we formulate a deterministic model for schistosomiasis transmission dynamics in order to explore the role of the several control strategies. The basic reproductive number is computed. Sufficient conditions for the global asymptotic stability of the disease-free equilibrium are obtained. By using the Center Manifold Theory, we analyze the local stability of endemic equilibrium. Finally, numerical simulations support our analytical conclusions and the sensitive analysis on the basic reproductive number to the changes of control parameters are shown. Our results imply that snail-killing is the most effective way to control the transmission of schistosomiasis.     

Periodicity detection on the parameter-space of a forced Chua’s circuit

We report a Periodicity-Detection algorithm, implemented in a LabVIEW routine for real-time data analysis on experimental chaos, to evaluate the periodicity P of experimental time series. The Periodicity-Detector (PD) algorithm was applied to the forced Chua’s circuit with the aim to build the Periodicity-parameter-space (P-parameter-space). As results of the P-parameter-space, we could observe very complex dynamical behaviors, as regions of periodic structures, a new sequence of accumulation boundary, and the periodic structures organizing themselves in a period-adding bifurcation cascade. Those results agree with the maximal Lyapunov exponent and the bifurcation diagram analysis, presented in a previous work.     

Nonlinear dynamics of an inclined beam subjected to a moving load

In this paper, the nonlinear dynamic response of an inclined pinned-pinned beam with a constant cross section, finite length subjected to a concentrated vertical force traveling with a constant velocity is investigated. The study is focused on the mode summation method and also on frequency analysis of the governing PDEs equations of motion. Furthermore, the steady-state response is studied by applying the multiple scales method. The nonlinear response of the beam is obtained by solving two coupled nonlinear PDEs governing equations of planar motion for both longitudinal and transverse oscillations of the beam. The dynamic magnification factor and normalized time histories of mid-pint of the beam are obtained for various load velocity ratios and the outcome results have been illustrated and compared to the results with those obtained from traditional linear solution. The appropriate parametric study considering the effects of the linear viscous damping, the velocity of the traveling load, beam inclination angle under zero or nonzero axial load are carried out to capture the influence of the effect of large deflections caused by stretching effects due to the beam’s immovable ends. It was seen that quadratic nonlinearity renders the softening effect on the dynamic response of the beam under the act of traveling load. Also in the case where the object leaves the inclined beam, its planar motion path is derived and the targeting accuracy is investigated and compared with those from the rigid solution assumption. Moreover, the stability analysis of steady-state response for the modes equations having quadratic nonlinearity was carried out and it was observed from the frequency response curves that for the considered parameters in the case of internal-external primary resonance, both saturation phenomenon and jump phenomenon can be predicted for the longitudinal excitation.     

Nonlinear dynamics of a non-autonomous network with coupled discrete–continuum oscillators

A network model of a multi-modular floating platform incorporated with a runway structure, viewed as a non-autonomous network with discrete–continuum oscillators, is developed for a general purpose of dynamic analysis. Numerical analysis shows the coupling effect between the two different types of oscillators on various complex dynamics, including sudden leaps, torus motions, beating vibrations, the synergetic effect of phase lock and anti-phase synchronizations. The amplitude death phenomenon, a suppressed weak oscillation state, is studied by using the fundamental solution derived by the averaging method. The parametric domain of the onset of amplitude death is illustrated to show the great significance to the stability design of the floating platform. The effect of the flexural rigidity of the runway on the distribution of amplitude death state is also discussed.     

Analytical bifurcation analysis of a rotor supported by floating ring bearings

Like with other types of fluid bearings, rotors supported by floating ring bearings may become unstable with increasing speed of rotation due to self-excited vibrations. In order to study the effects of the nonlinear bearing forces, within this contribution a perfectly balanced symmetric rotor is considered which is supported by two identical floating ring bearings. Here, the bearing forces are modeled by applying the short bearing theory for both fluid films. A linear stability analysis about the static equilibrium position of the rotor shows that for a critical revolution speed the real part of an eigenvalue pair changes its sign. By means of a center manifold reduction it is shown that this destabilization of the steady state is due to a Hopf-bifurcation. Furthermore, the type of this bifurcation is determined as well as the existence and stability of limit-cycles. Notably it is found that depending on the parameters of the floating ring bearing subcritical as well as supercritical bifurcations may occur. Additionally, the analytical results obtained from the center manifold reduction are compared to numerical results by a continuation method. In conclusion, the influences of bearing design parameters on the stability and on the limit-cycles are discussed.     

Influence of small harmonic terms on eigenvalues of monodromy matrix of piecewise-linear oscillators

In this paper we consider the problem which can appear at the determination of the dynamical stability of the responses of oscillators with discontinuous or steep derivative of the restoring characteristic obtained in the frequency domain. For that purpose, a simple one degree-of-freedom system with piecewise-linear force-displacement relationship subjected to a harmonic excitation is analysed. Stability of the periodic response obtained in the frequency domain by the incremental harmonic balance method is determined by using the Floquet-Liapounov theorem. Confirmation of the results obtained in the frequency domain is done by comparing with the results obtained in the time domain by the method of piecing the exact solutions. Determination of the dynamical stability can be made more reliable by using the proposed plot of maximum modulus of the eigenvalues of the monodromy matrix in dependence of non-dimensional frequency and the number of harmonics included in the supposed approximate solution.     

Relaxation oscillations,subharmonic orbits and chaos in the dynamics of a linear lattice with a local essentially nonlinear attachment

We study the dynamic interactions between traveling waves propagating in a linear lattice and a lightweight, essentially nonlinear and damped local attachment. Correct to leading order, we reduce the dynamics to a strongly nonlinear damped oscillator forced by two harmonic terms. One of the excitation frequencies is characteristic of the traveling wave that impedes to the attachment, whereas the other accounts for local lattice dynamics. These two frequencies are energy-independent; a third energy-dependent frequency is present in the problem, characterizing the nonlinear oscillation of the attachment when forced by the traveling wave. We study this three-frequency strongly nonlinear problem through slow-fast partitions of the dynamics and resort to action-angle coordinates and Melnikov analysis. For damping below a critical threshold, we prove the existence of relaxation oscillations of the attachment; these oscillations are associated with enhanced targeted energy transfer from the traveling wave to the attachment. Moreover, in the limit of weak or no damping, we prove the existence of subharmonic oscillations of arbitrarily large periods, and of chaotic motions. The analytical results are supported by numerical simulations of the reduced order model.     

Global stability of a delayed SEIRS epidemic model with saturation incidence rate

In this paper, an SEIRS epidemic model with a saturation incidence rate and a time delay describing a latent period is investigated. By analyzing the corresponding characteristic equations, the local stability of an endemic equilibrium and a disease-free equilibrium is established. When the basic reproduction number is greater than unity, by means of an iteration technique, sufficient conditions are obtained for the global asymptotic stability of the endemic equilibrium. By comparison arguments, it is proved that if the basic reproduction number is less than unity, the disease-free equilibrium is globally asymptotically stable. Numerical simulations are carried out to illustrate the main theoretical results.     

Effects of NAPL Contaminants on the Permeability of a Soil‐Bentonite Slurry Wall Material

Soilbentonite slurry walls are designed to inhibit the subsurface movement of contaminants from hazardous waste sites. Although it is generally accepted that high concentrations of organic compounds will adversely affect soilbentonite slurry walls and clay liners, previous research investigating the effects of NAPLs on the conductivity of clay wall materials has been inconclusive. In this study the effects of various organics (benzene, aniline, trichloroethylene, ethylene dichloride, methylene chloride) on the effective conductivity of a typical soilbentonite slurry wall material were studied under two effective stress conditions, 200 and 52kPa. The hydraulic conductivity for the soilbentonite material permeated with water averaged 1.52×10^-8cms^-1. Compared to water, there was little change in conductivity when the sample was permeated with a solution containing a NAPL compound at its solubility limit, except for aniline. However, there was a one to two order of magnitude decrease in conductivity when the sample was permeated with a pure NAPL for all NAPLs tested. When the soilbentonite material was permeated with a water/NAPL/water/NAPL sequence, the conductivity decreased one to two orders of magnitude when a NAPL was introduced following water; however, when water was reintroduced after the NAPL, the conductivity increased to the initial hydraulic conductivity. The conductivity again decreased one to two orders of magnitude when the NAPL was reintroduced. This trend occurred for all NAPLs tested, and the fluid properties of the NAPL compounds alone did not account for the decrease in conductivity compared to water.     

Hopf bifurcation analysis of a four-neuron network with multiple time delays

This paper reveals the dynamics of a neural network of four neurons with multiple time delays and a short-cut connection through a combined study of theoretical analysis, numerical simulations, and experiments. The first step of the study is to derive the sufficient conditions for the stability and instability of the network equilibrium, and the second step is to determine the properties of the periodic response bifurcating from a Hopf bifurcation of the network equilibrium on the basis of the normal form and the center manifold reduction. Afterwards, the study turns to the validation of theoretical results through numerical simulations and a circuit experiment. The case studies show that both numerical simulations and circuit experiment get a nice agreement with theoretical results.     

Complex dynamics analysis for a duopoly model of common fishery resource

In this paper, we formulate a dynamical model of commercial exploitations of renewable resources by assuming that two agents behave adaptively, following a bounded rationality adjustment process based on a local estimate of the marginal profit. We study the existence and the stability of the positive equilibrium characterizing the sustainable use of the renewable resource. Then we investigate the local bifurcations of the system through numerical simulation. We discover when one player accelerates the adjustment speed in order to achieve initial advantage, it may cause complex phenomena like quasi-period and chaos. Finally, we investigate a degraded two-dimensional system by showing the influence of the adjustment speed of the harvesting quantity on the set of initial conditions which give non-negative trajectories (called a feasible set). We find that higher adjustment speed may easily exhaust the resources.     

Effect of rotation on plane waves at the free surface of a fibre-reinforced thermoelastic half-space using the finite element method

The propagation of plane waves in fibre-reinforced, rotating thermoelastic half-space proposed by Lord-Shulman is discussed. The problem has been solved numerically using a finite element method. Numerical results for the temperature distribution, the displacement components and the thermal stress are given and illustrated graphically. Comparisons are made with the results predicted by the coupled theory and the theory of generalized thermoelasticity with one relaxation time in the presence and absence of rotation and reinforcement. It is found that the rotation has a significant effect and the reinforcement has great effect on the distribution of field quantities when the rotation is considered.     

Stochastic analysis of the electromagnetic induction effect on a neuron’s action potential dynamics

Nonlinear Dynamics - The presence of time-varying electromagnetic fields across a neuron cell may cause changes in its electrical characteristics, most notably, in the action potential dynamics....     

A velocity matching car-following model on a closed ring in which overtaking is allowed

Car-following models seek to describe the behaviour of a group of vehicles as they move along a stretch of road. In such models the behaviour of each vehicle is taken to be dependant on the motion of the vehicle in front and overtaking is not permitted. In this paper the effect of removing this ‘no-overtaking’ restriction is investigated. The resulting model is described in terms of a set of coupled time delay differential equations and these are solved numerically to analyse their post-transient behaviour under a periodic perturbation. For certain parameter choices this behaviour is found to be chaotic, and the degree of chaos is estimated using the Grassberger–Procaccia dimension.     

Extension of Lagrangian–Hamiltonian mechanics for continuous systems—investigation of dynamics of a one-dimensional internally damped rotor driven through a dissipative coupling

In this paper, the extended Lagrangian formulation for a one-dimensional continuous system with gyroscopic coupling and non-conservative fields has been developed. Using this formulation, the dynamics of an internally and externally damped rotor driven through a dissipative coupling has been studied. The invariance of the extended or so-called umbra-Lagrangian density is obtained through an extension of Noether’s theorem. The rotor shaft is modeled as a Rayleigh beam. The dynamic behavior of the rotor shaft is obtained and validated through simulation studies. Results show an interesting phenomenon of limiting behavior of the rotor shaft with internal damping beyond certain threshold speeds which are obtained theoretically and affirmed by simulations. It is further observed that there is entrainment of whirling speeds at natural frequencies of the rotor shaft primarily depending on the damping ratio.