Related Experiment Video
Updated: May 11, 2025
11:18
Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks
Published on: March 2, 2015
10.2K
A fractional-order multi-delayed bicyclic crossed neural network: Stability, bifurcation, and numerical solution
Pushpendra Kumar1, Tae H Lee1, Vedat Suat Erturk2
1Division of Electronic Engineering, Jeonbuk National University, Jeonju-Si, 54896, The Republic of Korea.
Summary
This study introduces a novel fractional-order bicyclic neural network (NN) with time delays. Researchers found that both time delay and derivative order impact NN stability and bifurcation, mimicking complex information transmission.
Area of Science:
- Computational Neuroscience
- Dynamical Systems Theory
- Fractional Calculus
Background:
- Neural networks (NNs) are crucial for modeling complex systems.
- Fractional-order dynamics offer a more nuanced approach to modeling memory and hereditary properties in NNs.
- Bicyclic structures with shared neurons present unique dynamic behaviors.
Purpose of the Study:
- To propose and analyze a novel fractional-order bicyclic crossed neural network (NN) with multiple time delays.
- To investigate the existence, uniqueness, boundedness, and stability of solutions for the proposed NN.
- To analyze the onset of Hopf bifurcation and the influence of time delays and fractional order on network dynamics.
Main Methods:
- Definition of the fractional-order NN using Caputo fractional derivatives.
- Analytical methods to prove boundedness and the existence of a unique solution.
- Stability and Hopf bifurcation analysis by reducing the multiple-delayed NN to a single-delay system.
- Numerical simulations using the L1 predictor-corrector algorithm.
Main Results:
- The proposed fractional-order bicyclic crossed NN with two sharing neurons between rings was successfully defined.
- Boundedness and the existence of a unique solution were analytically proven.
- The study demonstrated that both time delay and the order of the fractional derivative significantly influence the stability and bifurcation phenomena of the NN.
- Numerical simulations corroborated the theoretical findings.
Conclusions:
- The proposed fractional-order bicyclic crossed NN is a unique model for studying complex information transmission in networks.
- The interplay between time delays and fractional order is critical for understanding the stability and dynamic behaviors (bifurcation) of such intricate neural systems.
- The findings provide valuable insights into the design and analysis of advanced neural network models with memory effects.
Related Concept Videos
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