A hybrid approach for synchronizing between two reaction-diffusion systems of integer- and fractional-order applied on certain chemical models. (English) Zbl 1498.93696
Summary: In this study, a synchronization problem for spatio-temporal partial differential systems is addressed and researched within a subjectivist framework. In light of Lyapunov direct method and some proposed nonlinear controllers, a new scheme is established to accomplish a full synchronization between two reaction-diffusion systems of integer- and fractional-order. In particular, a novel vector-valued control law is analytically derived to attain the desired synchronization between two chemical models, namely, the Lengyel-Epstein and Gray-Scott models. To validate the obtained theoretical results, further numerical simulations are carried out in 2D and 3D configurations.
MSC:
| 93D99 | Stability of control systems |
| 93C20 | Control/observation systems governed by partial differential equations |
| 35K57 | Reaction-diffusion equations |
| 26A33 | Fractional derivatives and integrals |
Keywords:
complete synchronization; reaction-diffusion models; fractional-order system; chemical modelsReferences:
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