一个分数顺序的多延迟双循环交叉神经网络:稳定性,分叉和数值解决方案
Pushpendra Kumar1, Tae H Lee1, Vedat Suat Erturk2
1Division of Electronic Engineering, Jeonbuk National University, Jeonju-Si, 54896, The Republic of Korea.
概括
这项研究引入了一种具有时间延迟的小数顺序双循环神经网络 (NN). 研究人员发现,时间延迟和衍生顺序都会影响NN的稳定性和分叉,模仿复杂的信息传输.
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
- 分数微积分的计算.
背景情况:
- 神经网络 (NN) 对于建模复杂系统至关重要.
- 分数顺序动态为模拟NN的记忆和遗传性质提供了更细致的方法.
- 具有共享神经元的自行车结构呈现出独特的动态行为.
研究的目的:
- 提出和分析一个具有多个时间延迟的小数顺序双循环交叉神经网络 (NN).
- 调查拟议的NN.解决方案的存在,独特性,局限性和稳定性.
- 分析Hopf分叉的开始以及时间延迟和分数顺序对网络动态的影响.
主要方法:
- 使用卡普托的分数导数来定义小数次序NN.
- 分析方法来证明局限性和唯一解决方案的存在.
- 稳定性和Hopf分叉分析通过将多次延迟的NN减少到单次延迟系统.
- 使用L1预测-校正算法进行数值模拟.
主要成果:
- 提出的分数顺序双循环交叉NN与两个共享神经元之间的环被成功定义.
- 局限性和唯一解决方案的存在被分析证明.
- 该研究表明,时间延迟和分数导数的顺序都显著影响了NN的稳定性和分叉现象.
- 数字模拟证实了理论发现.
结论:
- 拟议的分数顺序双循环交叉NN是研究网络中复杂信息传输的独特模型.
- 时间延迟和分数顺序之间的相互作用对于理解这些复杂的神经系统的稳定性和动态行为 (分叉) 至关重要.
- 这些发现为设计和分析具有记忆效应的先进神经网络模型提供了宝贵的见解.
相关概念视频
01:25Multimachine Stability
101
Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
101
01:24Pole and System Stability
213
The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's...
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's...
213
01:26Linear Approximation in Frequency Domain
79
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....
79
01:24BIBO stability of continuous and discrete -time systems
294
System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
294
01:18Second Order systems II
62
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.
62
01:21Linear Approximation in Time Domain
56
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
56