A lattice Boltzmann model for reaction dynamical systems with time delay

Nonlinear reaction dynamical systems with time delay are investigated to evaluate the capability of the lattice Boltzmann model for delay differential dynamical systems. The stiff delay systems, multi-delay systems and two-dimensional partial delay differential equation are studied. Computation precise, efficiency, delay appearances are observed. The simulation results indicate that the lattice Boltzmann method is an innovative and effective numerical method to simulate the nonlinear delay differential dynamical systems.

[1]  Kuang Jiao-xun.  A Numerical Analysis of A Class of Stiff Delay Differential Equations , 2002 .

[2]  Stefano Boccaletti,et al.  Effect of a Variable Delay in delayed Dynamical Systems , 2001, Int. J. Bifurc. Chaos.

[3]  Matthaeus,et al.  Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[4]  Shi Bao-Chang,et al.  A New Lattice Bhatnagar--Gross--Krook Model for the Convection--Diffusion Equation with a Source Term , 2005 .

[5]  C. V. Pao,et al.  Monotone iterations for numerical solutions of reaction‐diffusion‐convection equations with time delay , 1998 .

[6]  Shi Bao-Chang,et al.  A new lattice Boltzmann model for incompressible magnetohydrodynamics , 2005 .

[7]  Y. Qian,et al.  Lattice BGK Models for Navier-Stokes Equation , 1992 .

[8]  Gábor Stépán,et al.  Updated semi‐discretization method for periodic delay‐differential equations with discrete delay , 2004 .

[9]  R. Benzi,et al.  The lattice Boltzmann equation: theory and applications , 1992 .

[10]  Sauro Succi,et al.  Recent Advances in Lattice Boltzmann Computing , 1995 .

[11]  Nengchao Wang,et al.  A unified thermal Lattice BGK model for Boussinesq equations , 2005 .

[12]  Shiyi Chen,et al.  Lattice Boltzmann computations for reaction‐diffusion equations , 1993 .

[13]  Shiyi Chen,et al.  LATTICE BOLTZMANN METHOD FOR FLUID FLOWS , 2001 .

[14]  Toshiyuki Koto,et al.  Method of lines approximations of delay differential equations , 2004 .

[15]  Pankaj Wahi,et al.  Galerkin Projections for Delay Differential Equations , 2005 .

[16]  B. Shi,et al.  Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method , 2002 .

[17]  He Zhenmin,et al.  EMC effect on p-A high energy collisions , 1991 .

[18]  Benzi,et al.  Extended self-similarity in numerical simulations of three-dimensional anisotropic turbulence. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  Qing Li,et al.  LBGK Simulations of Turing Patterns in CIMA Model , 2001, J. Sci. Comput..