Projective exponential anti-synchronisation of space–time discrete Lur’e oscillator networks with uncertain Markov jumps

This paper investigates global projective anti-synchronisation in the mean-square sense in the asymptotic and exponential schemes of space–time discrete Markovian Lur’e dynamical networks with uncertain transition probabilities and Dirichlet boundary values. The findings of this study are noteworthy with regard to global projective asymptotic and exponential anti-synchronisation in the mean-square sense for the proposed discrete Markovian networks. The networks incorporate the Lyapunov–Krasovskii functional, which includes a double sum representing the delay-dependent components. Furthermore, the findings of this study indicate that the global projective asymptotic and exponential anti-synchronisation of space–time discrete Markovian Lur’e dynamical networks with uncertain transition probabilities can be achieved through the design of small diffusion intensities. It was unexpected to discover that the uncertain transition probabilities have no influence on the conditions that guarantee the global projective asymptotic and exponential anti-synchronisation of the networks. This paper presents a framework for exploring the issues of global projective asymptotic or exponential anti-synchronisation for space–time discrete Markovian networks, with the objective of identifying potential applications in a range of contexts. In conclusion, an illustrative example is provided to demonstrate the efficacy of the aforementioned method.