Abstract: Two magnetic memristors are introduced to simulate electromagnetic induction and electromagnetic radiation respectively, and their effects on a novel compound exponential memristor coupled four-element Hopfield neural network are studied. By changing the internal parameters m₁ of the memritic synapse and the coupling intensity k₂, it is found that the new system has various different firing modes, such as periodic bursting firing, chaotic bursting firing, transient chaotic spiking firing, transient stochastic bursting firing, etc. By changing the initial value of the system, it is found that the new system produces five different coexisting firing modes, such as stochastic bursting firing, chaotic spiking firing, periodic spiking firing, etc. In addition, compared with the original system without electromagnetic induction and electromagnetic radiation, the new system also produces a wide range of hyperchaos and parameterless state switching. Finally, the hardware implementation of the new system is carried out by STM32 MCU.