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State feedback controllers based finite-time and fixed-time stabilisation of high order BAM with reaction–diffusion term

ABSTRACT In this paper, we are interested in the finite time and fixed-time stabilisation of high order bidirectional associative memory neural networks (HOBAMNNs) with time delays and reaction–diffusion terms. Via the theory of topological degree, a set of sufficient conditions are obtained to guarantee the existence of the equilibrium point of HOBAMNNs. The finite time and fixed time stabilisation are introduced based on Lyapunov functional, new designing state feedback controllers and inequality techniques. At the end, some numerical simulations are carried out to support the theoretical results.