复杂的自适应学习皮质神经网络系统用于解决带有爆发和混合模式振荡行为的时间微分方程
Yu-Ming Chu1, Saima Rashid2,3, Taher Alzahrani4
1Department of Mathematics, Huzhou University, Huzhou, 313000, China.
Scientific reports
|December 17, 2023
概括
伊希克维奇神经元模型中的分数顺序动态引入了依赖于记忆的行为,产生了对皮层神经元功能至关重要的多样化的尖端和爆发模式. 这项研究探讨了这些分数机制如何影响神经元属性和网络同步.
科学领域:
- 计算神经科学是一种神经科学.
- 复杂系统动力学 复杂系统动力学
- 生物物理学的生物物理.
背景情况:
- 皮层神经元在尖端分辨率下表现出复杂的输入-输出函数,此前的工作是探索对记忆依赖行为的分数计算.
- 特定的发射模式,如共振器的喋喋不休,快速的尖峰和混乱的爆发,对于神经元的处理至关重要,但小数次序动态的作用仍然不清楚.
研究的目的:
- 研究如何离散的分数顺序机制修改神经元的发射属性,特别是在Izhikevich神经元框架内.
- 用微分差方程分析神经元模型中各种共振和爆发模式的生成.
- 在分数指数下探索伊希基维奇神经元网络 (INN) 的动态行为,并展示稳定和同步的控制策略.
主要方法:
- 利用离散分数计算来建模伊希克维奇神经元框架,结合相称,非相称和可变顺序模式.
- 通过分割周期性解决方案来分析分叉,以了解神经元行为随时间的演变.
- 在计算和概念上使用分数差异方程调查破裂趋势,并检查可激发/抑制的INN与受调节的因子集.
主要成果:
- 证明伊希基维奇模型中的离散分数顺序动态可以产生皮质活动特征的广泛共振.
- 在受分数指数影响的分数顺序Izhikevich神经元网络中观察到各种爆发模式和独特的动态行为.
- 成功展示了动态控制器来稳定和同步拟议的分数顺序神经元框架.
结论:
- 在分数级动态中固有的记忆痕迹,整合过去的神经元活动,负责观察到的特殊尖端和爆发活动.
- 复杂的神经元动态,包括尖峰和爆发,源于细胞内和细胞外离子电流的长期依赖和复杂的相互作用.
- 分数顺序建模为理解皮层神经元丰富且依赖于记忆的行为提供了一个强大的框架.
相关概念视频
Classification of Systems-II
149
Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
149
RLC Circuit as a Damped Oscillator
1.0K
An RLC circuit combines a resistor, inductor, and capacitor, connected in a series or parallel combination.
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...
1.0K
Ampere-Maxwell's Law: Problem-Solving
634
A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
To solve the problem, we can use the equations from the analysis of an RC circuit and Maxwell's version of Ampère's law.
For the first part of...
To solve the problem, we can use the equations from the analysis of an RC circuit and Maxwell's version of Ampère's law.
For the first part of...
634
Neural Circuits
1.3K
Neural circuits and neuronal pools are two of the main structures found in the nervous system. Neural circuits are networks of neurons that work together to carry out a specific task or process. They consist of interconnected neurons and glial cells, which provide structural and metabolic support.
Neuronal pools are collections of nerve cells with similar functions and interact through chemical and electrical signals. These pools include both interneurons (the central neural circuit nodes that...
Neuronal pools are collections of nerve cells with similar functions and interact through chemical and electrical signals. These pools include both interneurons (the central neural circuit nodes that...
1.3K
Current Growth And Decay In RL Circuits
3.8K
The current growth and decay in RL circuits can be understood by considering a series RL circuit consisting of a resistor, an inductor, a constant source of emf, and two switches. When the first switch is closed, the circuit is equivalent to a single-loop circuit consisting of a resistor and an inductor connected to a source of emf. In this case, the source of emf produces a current in the circuit. If there were no self-inductance in the circuit, the current would rise immediately to a steady...
3.8K
Difference Equation Solution using z-Transform
297
The z-transform is a powerful tool for analyzing practical discrete-time systems, often represented by linear difference equations. Solving a higher-order difference equation requires knowledge of the input signal and the initial conditions up to one term less than the order of the equation.
The z-transform facilitates handling delayed signals by shifting the signal in the z-domain, which corresponds to delaying the signal in the time domain, and advancing signals by similarly shifting in the...
The z-transform facilitates handling delayed signals by shifting the signal in the z-domain, which corresponds to delaying the signal in the time domain, and advancing signals by similarly shifting in the...
297


