Narrow Results

Controlling neurons to generate a desired or normal spiking behavior is the fundamental building block of the treatment of many neurologic diseases. The objective of this work is to develop a novel control method–closed-loop proportional integral (PI)-type iterative learning control (ILC) algorithm to control the spiking behavior in model neurons. In order to verify the feasibility and effectiveness of the proposed method, two single-compartment standard models of different neuronal excitability are specifically considered: Hodgkin–Huxley (HH) model for class 1 neural excitability and Morris–Lecar (ML) model for class 2 neural excitability. ILC has remarkable advantages for the repetitive processes in nature. To further highlight the superiority of the proposed method, the performances of the iterative learning controller are compared to those of classical PI controller. Either in the classical PI control or in the PI control combined with ILC, appropriate background noises are added in neuron models to approach the problem under more realistic biophysical conditions. Simulation results show that the controller performances are more favorable when ILC is considered, no matter which neuronal excitability the neuron belongs to and no matter what kind of firing pattern the desired trajectory belongs to. The error between real and desired output is much smaller under ILC control signal, which suggests ILC of neuron’s spiking behavior is more accurate.

In this paper, a novel meshless numerical scheme to solve the time-fractional Oskolkov–Benjamin–Bona–Mahony–Burgers-type equation has been proposed. The proposed numerical scheme is based on finite difference and Kansa-radial basis function collocation approach. First, the finite difference scheme has been employed to discretize the time-fractional derivative and subsequently, the Kansa method is utilized to discretize the spatial derivatives. The stability and convergence analysis of the time-discretized numerical scheme are also elucidated in this paper. Moreover, the Kudryashov method has been utilized to acquire the soliton solutions for comparison with the numerical results. Finally, numerical simulations are performed to confirm the applicability and accuracy of the proposed scheme.

The novelty of this contribution is to propose an implicit numerical scheme for solving time-dependent boundary layer problems. The scheme is multi-step and consists of two stages. It is third-order accurate in time and constructed on three-time levels. For spatial discretization, a fourth-order compact scheme is adopted. The stability of the proposed scheme is analyzed for scalar linear partial differential equation (PDE) that shows its conditional stability. The convergence of the scheme is also provided for a system of time-dependent parabolic equations. Moreover, a mathematical model for heat and mass transfer of mixed convective Williamson nanofluid flow over flat and oscillatory sheets is modified with the characteristic of the Darcy–Forchheimer model. The results show that the temperature profile rises by developing thermophoresis and Brownian motion parameter values. Also, the proposed scheme is compared with an existing Crank–Nicolson method. It is found that the proposed scheme converges faster than the existing one for solving scalar linear PDE as well as the system of linear and nonlinear parabolic equations, which are dimensionless forms of governing equations of a flow phenomenon. The findings provided in this study can serve as a helpful guide for future investigations into fluid flow in closed-off industrial settings.