Mathematical analysis and modeling of fractional order human brain information dynamics including the major effect on sensory memory

Abstract

In this work, we propose fractional-order deterministic mathematical models for human brain information dynamics, including the major effect on sensory memory. The two models are top-down and bottom-up processing. Mathematical models are analysed for different cases for long and short-term memory effects with the effect of experience and prior knowledge. Studies are conducted both qualitatively and quantitatively to analyse systems using fixed-point theory results. The impact of the global derivative, linear growth, and Lipschitz criteria are used to check the existence and uniqueness of the model for the biological feasibility of the system. Positivity and boundedness of the unique solution were also treated. The global stability of the proposed model is constructed by constructing the first and second derivatives for the Lyapunov function using wave analysis according to the equilibrium point. Numerical simulations of the proposed method in the range of fractional orders are conducted to demonstrate the implications of fractional and fractal orders. To further explore the impact of various parameters on the information processing process in the human brain, information in long-term memory, repetition, and rehearsal Chaotic modelling of the brain information dynamics model is also derived for different cases that are stable and bound to feasible regions. Results demonstrate the strong memory effect by using nonlocal and non-singular kernels at different fractional order values and fractal dimensions, which support experimental and theoretical observations.

Keywords:

• Sensory memory model
• well posedness
• uniqueness
• stability analysis
• fractal fractional
• numerical approximation

REVIEWING EDITOR:

• Zhongmin Jin, Xian Jiao Tong University (China) and Leeds University (UK)

SUBJECTS:

• Mathematical Numerical Analysis; Applied Mathematics; Mathematical Biology

Disclosure statement

No potential conflict of interest was reported by the author(s).

Figure 9. Chaotic modeling of Brain Information dynamics model for case 1 bounded to feasible region.

Figure 10. Chaotic modeling of Brain Information dynamics model for case 2 bounded to feasible region.

Figure 11. Chaotic modeling of Brain Information dynamics model for case 1 bounded to feasible region.

Figure 12. Chaotic modeling of Brain Information dynamics model for case 2 bounded to feasible region.

Table 1. Parameter values.

Additional information

Funding

Prince Sattam bin Abdulaziz University for funding this research: project number (PSAU/2023/01/2189822).