声明
Chapter 1 Introduction
1.1 Fractals
1.1.1 Fractals in Nature
1.1.2 Fractals Geometry
1.1.3 Fractals Properties
1.1.4 Fractals Applications
1.1.5 Conclusions
1.2 Research Objectives
1.3 Methodology
1.4 Dissertation Structure
Chapter 2 Fixed-Parameter Neural Dynamics Fractals
2.1 Model of Fixed Parameter Neural Dynamics
2.1.1 Relate to Newton Iterations
2.2 Fractals Generating
2.2.1 Newton Fractals
2.2.2 FP-DTCVND Fractals
2.3 Varying-Parameters Convergent-Differential Neural-Network (VP-CDNN)
2.3.1 VP-CDNN Model
2.3.2 Comparison with FT-ZNN
Chapter 3 Exponential-Type Varying-Parameter Neural Dynamics Fractals
3.1 Model of the Exponential-Type Varying-Parameter Neural Dynamics
3.1.1 Varying-Parameters Discrete Time Complex-Valued Neural (YP-DTCVND)
3.1.2 Model for Solving Static Nonlinear Equations
3.2 Exponential-Type VP-DTCVND Fractals Generating
3.2.2 Fractals via f(z,t)=sin(z)+exp(z)-sin(t)-i·t=0
3.2.3 Fractals via f(z,t)=exp(z)7+i·cos(t)=0
3.3 Comparing between Fractals of FP-DTCVND and the Exponential-Type VP-DTCVND
3.3.1 Comparison Considering the Linear Activation Function
3.3.2 Comparison Considering the Power-sum Activation Function
3.3.3 Comparison Considering the Power-sigmoid Activation Function
3.3.4 Comparison Considering the Hyperbolic-sine Activation Function
3.3.5 Comparison between the Activation Function Performance
Chapter 4 Power-Type Varying-Parameter Neural Dynamics Fractals
4.1 Power-Type VP-DTCVND Model
4.1.1 Different Activation Functions
4.1.2 Model for Solving Static Nonlinear Equations
4.1.3 Comparison between Convolution Models
4.2 Power-Type VP-DTCVND Fractals Generating
4.2.2 Fractals via f(z)=cos(2s)=0
4.2.3 Fractals via f(z)=z3exp(z3+i)=0
4.2.4 Fractals via f(z,t)=z(t)3+exp(z)3+i·t=0
4.2.5 Fractals via f(z,t)=exp(z)+z(t)2-exp(t)-i·t=0
4.2.6 Fractals via f(z,t)=sin(z)+z(t)2-sin(t)-i·t=0
4.3 Comparing between Fractals of FP-DTCVND and the power-Type VP-DTCVND
4.3.1 Comparison Considering the Linear Activation Function
4.3.2 Comparison Considering the Power-sum Activation Function
4.3.3 Comparison Considering the Power-sigmoid Activation Function
4.3.4 Comparison Considering the Hyperbolic-sine Activation Function
4.3.5 Comparison between the Activation Function Performance
Chapter 5 Conclusion
5.1 Contributions Highlight
5.2 Future Work
参考文献
攻读硕士学位期间取得的研究成果
致谢
答辩决议书
华南理工大学;
