Neurons with Hidden Attractor via Only One Controller

Compared with the integer-order neuron model, the fractional-order neuron model can depict richer electrical activities of the neuron system and becomes a hot topic. To better understand the complex phenomenon of neuron, according to Caputo’s fractional derivative operator, the fractional-order Hindmarsh-Rose neuron model is introduced, and dynamics of it are investigated. Firstly, the hidden attractor of the proposed model is discussed via theoretical analysis and numerical simulation. Secondly, synchronization between fractional-order Hindmarsh-Rose neurons is realized by designing one controller whether the order is the same or different. Simultaneously, the impact of the order on the synchronization speed of considered systems with the same order is explored, and it is found that lower order is beneficial for speeding up synchronization. Theoretical results are confirmed via numerical simulations. Research results contribute to reveal some complex phenomena of neuron systems and control the complex dynamics effectively.