Bifurcation diagram

About: Bifurcation diagram is a research topic. Over the lifetime, 8379 publications have been published within this topic receiving 139664 citations.

Bifurcation Analysis of an SIRS Epidemic Model with Generalized Incidence

Abstract: An SIRS epidemic model, with a generalized nonlinear incidence as a function of the number of infected individuals, is developed and analyzed. Extending previous work, it is assumed that the natural immunity acquired by infection is not permanent but wanes with time. The nonlinearity of the functional form of the incidence of infection, which is subject only to a few general conditions, is biologically justified. The stability analysis of the associated equilibria is carried out, and the threshold quantity ($\R$) that governs the disease dynamics is derived. It is shown that $\R$, called the basic reproductive number, is independent of the functional form of the incidence. Local bifurcation theory is applied to explore the rich variety of dynamical behavior of the model. Normal forms are derived for the different types of bifurcation that the model undergoes, including Hopf, saddle-node, and Bogdanov--Takens. The first Lyapunov coefficient is computed to determine various types of Hopf bifurcation, such a...

Relaxation of a dewetting contact line. Part 2. Experiments

Abstract: The dynamics of receding contact lines is investigated experimentally through controlled perturbations of a meniscus in a dip-coating experiment. We first describe stationary menisci and their breakdown at the coating transition. Above this transition where liquid is deposited, it is found that the dynamics of the interface can be interpreted as a quasi-steady succession of stationary states. This provides the first experimental access to the entire bifurcation diagram of dynamical wetting, confirming the hydrodynamic theory developed in Part 1. In contrast to quasi-static theories based on a dynamic contact angle, we demonstrate that the transition strongly depends on the large-scale flow geometry. We then establish the dispersion relation for large wavenumbers, for which we find a decay rate σ proportional to wavenumber |q|. The speed dependence of σ is described well by hydrodynamic theory, in particular the absence of diverging time scales at the critical point. Finally, we highlight some open problems related to contact angle hysteresis that lead beyond the current description.

Experimental Study of a Symmetrical Piecewise Base-Excited Oscillator

Abstract: This paper presents an experimental study on a base-excited piecewise linear oscillator with symmetrical flexible constrains of high stiffness ratio (above 20). The details of the adopted design of the oscillator, the experimental set-up, and calibration procedure are briefly discussed. The regions of chaotic motion predicted theoretically were confirmed by the experimental results arranged into bifurcation diagram Clearance, stiffness ratio, amplitude, and frequency of the external force were used as branching parameters. The discussion of the system dynamics is based on bifurcation diagrams and Lissajous curves. The investigated system tends to be periodic for large clearances and chaotic for small ones. This picture is reversed for the amplitude of the forcing change where periodic motion occurred for small values and chaos dominated for larger forcing. The same behavior is observed for increasing frequency ratio where, for values below the natural frequency, the most interesting dynamics occurs. For the investigated parameter values, the stiffness ratio variation produces only periodic motion.

Numerical analysis of a fractional-order chaotic system based on conformable fractional-order derivative

Abstract: In this paper, the numerical solutions of conformable fractional-order linear and nonlinear equations are obtained by employing the constructed conformable Adomian decomposition method (CADM). We found that CADM is an effective method for numerical solution of conformable fractional-order differential equations. Taking the conformable fractional-order simplified Lorenz system as an example, the numerical solution and chaotic behaviors of the conformable fractional-order simplified Lorenz system are investigated. It is found that rich dynamics exist in the conformable fractional-order simplified Lorenz system, and the minimum order for chaos is even less than 2. The results are validated by means of bifurcation diagram, Lyapunov characteristic exponents and phase portraits.