LOCALIZED PATTERNS OF THE CUBIC-QUINTIC SWIFT-HOHENBERG EQUATIONS WITH TWO SYMMETRY-BREAKING TERMS

Homoclinic snake always refers to the branches of homoclinic orbits near a heteroclinic cycle connecting a hyperbolic or non-hyperbolic equilibrium and a periodic orbit in a reversible variational system. In this paper, the normal form of a Swift-Hohenberg equation with two different symmetry-breaking terms （non-reversible term and non-k-symmetry term） are investigated by using multiple scale method, and their bifurcation diagrams are initially studied by numerical simulations. Typically, we predict numerically the existence of so- called round-snakes and round-isolas upon particular two symmetric-breaking perturbations.

LOCALIZED PATTERNS OF THE SWIFT-HOHENBERG EQUATION WITH A DISSIPATIVE TERM

In this paper, the normal form analysis of quadratic-cubic Swift-Hohenberg equation with a dissipative term is investigated by using the multiple-scale method. In addition, we obtain Hamiltonian-Hopf bifurcations of two equilib- ria and homoclinic snaking bifurcations of one-peak and two-peak homoclinic solutions by numerical simulations.

TRAVELING WAVE SOLUTIONS AND THEIR STABILITY OF NONLINEAR SCHRDINGER EQUATION WITH WEAK DISSIPATION

In this paper,several new constant-amplitude and variable-amplitude wave solutions（namely,traveling wave solutions） of a generalized nonlinear Schrdinger equation are investigated by using the extended homogeneous balance method,where the balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation,respectively.In addition,stability analysis of those solutions are also conducted by regular phase plane technique.

Suspected Close Contacts as the Pilot Indicator of the Growth Trend of Confirmed Population During the COVID-19 Pandemic: A Simulation Approach

Regarding to the actual situation of the new coronavirus disease 2019 epidemic,social factors should be taken into account and the increasing growth trend of confirmed populations needs to be explained.A proper model needs to be established,not only to simulate the epidemic,but also to evaluate the future epidemic situation and find a pilot indicator for the outbreak.The original susceptible-infectious-recover model is modified into the susceptible-infectious-quarantine-confirm-recover combined with social factors(SIDCRL)model,which combines the natural transmission with social factors such as external interventions and isolation.The numerical simulation method is used to imitate the change curve of the cumulative number of the confirmed cases and the number of cured patients.Furthermore,we investigate the relationship between the suspected close contacts(SCC)and the final outcome of the growth trend of confirmed cases with a simulation approach.This article selects four representative countries,that is,China,South Korea,Italy,and the United States,and gives separate numerical simulations.The simulation results of the model fit the actual situation of the epidemic development and reasonable predictions are made.In addition,it is analyzed that the increasing number of SCC contributes to the epidemic outbreak and the prediction of the United States based on the population of the SCC highlights the importance of external intervention and active prevention measures.The simulation of the model verifies its reliability and stresses that observable variable SCC can be taken as a pilot indicator of the coronavirus disease 2019 pandemic.