Abstract
We investigate the generalized projective synchronization (GPS) control of fractional-order extended Hindmarsh-Rose (FOEHR) neuronal models with transcranial magneto-acoustical stimulation (TMAS) input. This improved neuronal model has advantages in describing the complex firing characteristics of neurons stimulated by alternating current. In this study, a master-slave neuron system consisting of two FOEHR neuronal models is assumed to be subject to uncertain model parameters and unknown external disturbances. To quantify the GPS error, we design a new error variable based on the properties of the fractional-order derivative and construct a related GPS error system. Fuzzy logic systems are introduced to approximate the unknown nonlinear dynamics of the error system. To ensure the synchronous firing rhythms of the master-slave neuron system, an adaptive fuzzy control algorithm is proposed under the Lyapunov approach, in which the adaptive parameters are robust to the estimation errors. By choosing the appropriate design parameters, the proposed control scheme enables the master-slave neuron system to achieve GPS in a finite amount of time and to be resilient to uncertain parameters and unknown disturbances. The simulation results demonstrate that after the designed control inputs are implemented, the states of the slave neuron synchronize with those of the master neuron in specified proportions, and the corresponding synchronization error converges towards an arbitrarily small neighborhood of zero.
Highlights
Computational neuroscience plays a crucial role in the understanding of processes in the brain, as it is difficult to identify the actual interactions among neurons in a living brain
For the stimulus input Iext, the fixed parameters for tissue fluid and ultrasonic speed are chosen according to Table 1, and the adjustable magneto-acoustic parameters are fixed at Bx = 0.5, u = 1.0 and fu = 350; the exact current can be obtained by equation (9)
Adam-Bashforth-Moulton method is applied for the approximate solutions of the fractional-order differentiations and the fractional orders of the master and the slave neuronal models are set to q1 = 0.98 and q2 = 0.95, respectively
Summary
Computational neuroscience plays a crucial role in the understanding of processes in the brain, as it is difficult to identify the actual interactions among neurons in a living brain. With the development of computational neuroscience, various neuronal models that represent the biological characteristics of neurons have been proposed, such as the Hodgin-Huxley (HH) [2], FitzHugh-Nagumo (FHN) [3], The associate editor coordinating the review of this manuscript and approving it for publication was Zhiguang Feng. The classical HR neuronal model consists of three variables that represent the membrane potential, the spiking or recovery behavior, and the adaptation current passing through the slow channel, respectively [6], [7]. As research on the biological characteristics of neurons develops, some modified HR neuronal models have been introduced. Vepa et al proposed an extended HR neuron model consisting of four variables, in which the introduced
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