Volume 44 Issue 4
Apr.  2023
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LI Jian. Bistable Periodic Traveling Wave Solutions to Lattice Competitive Systems[J]. Applied Mathematics and Mechanics, 2023, 44(4): 471-479. doi: 10.21656/1000-0887.430071
Citation: LI Jian. Bistable Periodic Traveling Wave Solutions to Lattice Competitive Systems[J]. Applied Mathematics and Mechanics, 2023, 44(4): 471-479. doi: 10.21656/1000-0887.430071

Bistable Periodic Traveling Wave Solutions to Lattice Competitive Systems

doi: 10.21656/1000-0887.430071
  • Received Date: 2022-03-07
  • Rev Recd Date: 2022-04-11
  • Publish Date: 2023-04-01
  • The existence of bistable periodic traveling wave solutions to lattice competitive systems was studied. Firstly, the lattice competitive system of 2 species was transformed into a cooperative system. Then, the principle of comparison was established and a pair of upper and lower solutions were given to obtain the convergence of the solution at infinity, with the initial function satisfying certain conditions. By means of the vanishing viscosity method and the principle of comparison, the existence of the traveling wave solution connecting 2 stable periodic equilibrium points of the system, was proved.
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