Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   study coupled nonidentical Lorenz equations with three dierent boundary conditions. Coupling rules and boundary conditions play essential roles in the qualitative analysis of solutions of coupled systems. By using Lyapunov stability theory, a sucient condition is obtained for the global stability of trivial equilibrium of coupled system with Dirichlet condition. Then  restrict our attention on the dynamics of coupled nonidentical Lorenz equations with Neumann/periodic boundary condition and prove that the asymptotic synchronization occurs provided the coupling strengths are suciently large. That is, the dierence beten any two components of solution is bounded by the quantityO("= maxfc1 ;c 2 ;c 3g) as t!1, where " is the maximal deviation of parameters of nonidentical Lorenz equations, and c1,c2 and c3 are the specied coupling strengths.
['Chuang-Hsiung Chiu', 'Wen-Wei Lin', 'Chen-Chang Peng']
I am writing a research paper on a idea Asymptotic synchronization in lattices of coupled nonidentical Lorenz equations
[{"from": "human", "value": "I am writing a research paper on a idea Asymptotic synchronization in lattices of coupled nonidentical Lorenz equations"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   study coupled nonidentical Lorenz equations with three dierent boundary conditions. Coupling rules and boundary conditions play essential roles in the qualitative analysis of solutions of coupled systems. By using Lyapunov stability theory, a sucient condition is obtained for the global stability of trivial equilibrium of coupled system with Dirichlet condition. Then  restrict our attention on the dynamics of coupled nonidentical Lorenz equations with Neumann/periodic boundary condition and prove that the asymptotic synchronization occurs provided the coupling strengths are suciently large. That is, the dierence beten any two components of solution is bounded by the quantityO(\"= maxfc1 ;c 2 ;c 3g) as t!1, where \" is the maximal deviation of parameters of nonidentical Lorenz equations, and c1,c2 and c3 are the specied coupling strengths."}]