Explicit analytical solutions of higher-dimensional chaotic and hyperchaotic systems are areas of research to be much explored. Till now, the dynamics of higher-dimensional systems and the synchronisation dynamics of coupled higher-dimensional systems have not been studied analytically. In the present work, explicit analytical solutions are developed for the dynamical behaviours observed in third-order and fourth-order nonlinear dissipative systems and also for the coupled dynamics of these systems.The Chua’s circuit and the modified canonical Chua’s circuit are studied analytically in the present work. The analytical results explaining the underlying important features of these systems are validated through experimental results.