Yan Jia-Ren

Epidemic Dynamics with Feedback Mechanism in Exponential Networks

We introduce a feedback mechanism to study the spreading of an epidemic by analytical methods and large scale simulations in exponential networks. It is found that introducing the feedback mechanism can reduce the density of infected individuals. Furthermore, it does not change the epidemic threshold (critical point) λc. These results can help us to understand epidemic spreading phenomena on social networks more practically and design appropriate strategies to control social infections.

Solutions, bifurcations and chaos of the nonlinear Schrödinger equation with weak damping

Using the wave packet theory, we obtain all the solutions of the weakly damped nonlinear Schrodinger equation. These solutions are the static solution and solutions of planar wave, solitary wave, shock wave and elliptic function wave and chaos. The bifurcation phenomenon exists in both steady and non-steady solutions. The chaotic and periodic motions can coexist in a certain parametric space region.

Suppressing chaos by parametric perturbation at doubled frequency of periodic perturbation

An analysis of the chaos suppression of a nonlinear elastic beam (NLEB) is presented. In terms of modal transformation the equation of NLEB is reduced to the Duffing equation. It is shown that the chaotic behaviour of the NLEB is sensitively dependent on the parameters of perturbations and initial conditions. By adjusting the frequency of parametric perturbation to twice that of the periodic one and the amplitude of parametric perturbation to the same as the periodic one, the chaotic region of the nonlinear elastic beam driven by periodic force can be greatly suppressed.

Moving nonlinear localized modes for one-dimensional Klein-Gordon diatomic lattice

We study analytically the moving nonlinear localized vibrational modes (discrete breathers) for a one-dimensional Klein-Gordon diatomic lattice in the whole omega (q) plane of the system by means of a semi-discrete approximation, in which the carrier wave of the modes is treated explicitly while the envelope is described in the continuum approximation. We find that both pulse and kink envelope moving modes for this lattice system can occur with certain carrier wave vectors and vibrational frequencies in separate regions of the omega (q) plane. However, the kink envelope moving modes have not been reported previously for this lattice system.

Attack Vulnerability of Network with Duplication-Divergence Mechanism

We study the attack vulnerability of network with duplication-divergence mechanism. Numerical results have shown that the duplication-divergence network with larger retention probability σ is more robust against target attack relatively. Furthermore, duplication-divergence network is broken down more quickly than its counterpart BA network under target attack. Such result is consistent with the fact of WWW and Internet networks under target attack. So duplication-divergence model is a more realistic one for us to investigate the characteristics of the world wide web in future. We also observe that the exponent γ of degree distribution and average degree are important parameters of networks, reflecting the performance of networks under target attack. Our results are helpful to the research on the security of network.

Effect of Higher-Order Terms on Nonlinear Schrödinger Dark Solitons in Optical Fibres

We solve the nonlinear Schrodinger equation with higher order terms, which describes the propagation of femtosecond pulses in optical fibres, by means of a direct perturbation method for dark solitons. An exact dark-soliton solution of the higher order nonlinear Schrodinger equation is found, provided that parameters satisfy certain conditions. The solitons velocity with the high order effects as well as the formula for calculation of the first-order correction representing the perturbation-induced radiative field is presented.

A Special Two-Soliton Solution of sine-Gordon Equation

A special two-soliton solution of sine-Gordon equation is obtained by using the Hirota direct method. It is shown in a mass-centre system how two kinks move and interact with each other.

A certain critical two-soliton solution of the nonlinear Schr?dinger equation

An exact two-soliton solution of the nonlinear Schrodinger equation is derived by using the Hirota direct approach. This solution describes such a critical process that two still solitons separated infinitely approach and then pass through each other and keep straight on infinitely.

Bose-Einstein condensation in a spherical symmetric harmonic trap

Using a perturbation theory approach, we derive an approximate analytical solution of the Gross-Pitaevskii equation in a spherical symmetric harmonic trap. This solution is consistent with that obtained numerically.

Exact Nonstationary Solutions of a Two-Component Bose?Einstein Condensate

We investigate the exact nonstationary solutions of a two-component Bose–Einstein condensate which compose of two species having different atomic masses. We also consider the interesting behavior of the atomic velocity and the flow density. It is shown that the motion of the two components can be controlled by the experimental parameters.