侧面强迫对主FitzHugh-Nagumo神经元模型和单向合的双神经元系统的全球动态的影响
Nívea D Bosco1, Paulo C Rech1, Marcus W Beims2
1Departamento de Física, Universidade do Estado de Santa Catarina, 89219-710 Joinville, Brazil.
Chaos (Woodbury, N.Y.)
|September 19, 2024
概括
这项研究探讨了结合的菲茨休-纳古莫神经元模型. 主神经元是主要的神经元.
科学领域:
- 计算神经科学是一种神经科学.
- 动态系统理论 动态系统理论
- 非线性动力学是一种非线性动力学.
背景情况:
- 菲茨休-纳古莫模型是一个简化的神经元激发的数学模型.
- 结合的神经元动态对于理解神经网络行为至关重要.
- 研究主-奴隶配置揭示了神经系统中复杂的新兴特性.
研究的目的:
- 分析一个七参数,五维的动态系统,包括单向合的菲茨休-纳古莫神经元模型.
- 阐明主神经元 (N1) 动态模式 (周期性,准周期性,混乱性) 对合系统行为的影响.
- 将参数平面映射出来,并在合系统中识别不同的动态区域.
主要方法:
- 一个单向的主奴FitzHugh-Nagumo神经元系统的数值调查.
- 系统地探索从七维参数空间的截面中得出的参数平面.
- 在主神经元的三个不同的模式中分析系统动态:周期性,准周期性和混乱性.
主要成果:
- 在N1的周期系统中,合系统表现出周期添加的阿诺德舌状结构和多稳定性.
- 在N1的半周期状态中,周期运动是不存在的;只观察到半周期和混乱的动态.
- 在N1的混乱状态中,参数平面揭示了混乱,超级混乱和暂时超级混乱的区域.
结论:
- 主神经元的动态模式显著地决定了结合的菲茨休-纳古莫系统的行为.
- 参数平面分析有效地可视化复杂的动态现象,包括阿诺德舌头,多稳定性和超级混乱.
- 这项研究提供了各种强迫条件下的合神经模型复杂动态的见解.
相关概念视频
Forced Oscillations
6.5K
When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.
6.5K
Second Order systems II
93
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
93
Graphical and Analytic Representation of Sinusoids
379
Analyzing two sinusoidal voltages with equal amplitude and period but different phases on an oscilloscope, an instrument used to display and analyze waveforms, involves a three-step process.
The first step is measuring the peak-to-peak value, which is twice the amplitude of the sinusoid. This provides information about the maximum voltage swing of the waveform.
Secondly, the period and angular frequency are determined. The period is the time taken for one complete cycle of the waveform, while...
The first step is measuring the peak-to-peak value, which is twice the amplitude of the sinusoid. This provides information about the maximum voltage swing of the waveform.
Secondly, the period and angular frequency are determined. The period is the time taken for one complete cycle of the waveform, while...
379
Sinusoidal Sources
484
Direct current (DC) refers to an electric current that flows in a single direction, maintaining a constant polarity. This is in contrast to alternating current (AC), which periodically changes its direction and magnitude. AC forms the backbone of modern electricity transmission and distribution systems due to its efficient long-distance transmission capabilities.
In homes, the power supplies use sinusoidal sources to provide electricity. These sources generate a voltage that varies sinusoidally...
In homes, the power supplies use sinusoidal sources to provide electricity. These sources generate a voltage that varies sinusoidally...
484
Exponential and Sinusoidal Signals
245
The exponential function is crucial for characterizing waveforms that rise and decay rapidly. This continuous-time exponential function is defined using exponential terms with constants α and A. When both constants are real, the function is represented as,
245
Linear Approximation in Frequency Domain
88
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
88


