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Figure 8 Purelin Activation Function. Purelin is a linear transfer function used by neural networks and it is mathematically expressed as follows:

Figure 8 Purelin Activation Function. Purelin is a linear transfer function used by neural networks and it is mathematically expressed as follows:

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Figure 2 The phase portraits of Rucklidge chaotic system using Euler’s numerical solution.
Figure 2 The phase portraits of Rucklidge chaotic system using Euler’s numerical solution.
Figure 1 The time series of Rucklidge chaotic system using Eu- ler’s numerical solution.
Figure 1 The time series of Rucklidge chaotic system using Eu- ler’s numerical solution.
Figure 3 Artificial Neuron Structure Artificial Neural Network (ANN), is a computer algorithm in- spired by the neuron system in order to imitate the process of producing new information with learning in the human brain. It has been developed so that machines can recognize the desired pattern in complex data and generally performs better than other algorithms when recognizing audio, image or video segments. An ANN consists of inputs (X), weights (W), addition function, activa- tion function (Tansig, Purelin, Satlins etc.) and outputs. In ANN modeling, the relationship between Inputs (X) and Outputs (Y) is Y = f(X) +b. Here Weight (W) information is used to reduce the error (b).
Figure 3 Artificial Neuron Structure Artificial Neural Network (ANN), is a computer algorithm in- spired by the neuron system in order to imitate the process of producing new information with learning in the human brain. It has been developed so that machines can recognize the desired pattern in complex data and generally performs better than other algorithms when recognizing audio, image or video segments. An ANN consists of inputs (X), weights (W), addition function, activa- tion function (Tansig, Purelin, Satlins etc.) and outputs. In ANN modeling, the relationship between Inputs (X) and Outputs (Y) is Y = f(X) +b. Here Weight (W) information is used to reduce the error (b).
In Layered-Recurrent Neural Networks, the outputs in the hidden layers and the output layers are also fed back as inputs. Thus, it has a bidirectional working principle. Since there is feedback, this type of ANNs have memory. It is shown in Fig 5 “igure 5 The structure of Layered-Recurrent Neural Network
In Layered-Recurrent Neural Networks, the outputs in the hidden layers and the output layers are also fed back as inputs. Thus, it has a bidirectional working principle. Since there is feedback, this type of ANNs have memory. It is shown in Fig 5 “igure 5 The structure of Layered-Recurrent Neural Network
Figure 4 The structure of Feed-Forward Backpropagation Neural Network In this network structure, the information received from the in- puts is transmitted to the hidden layer and has a one-way working principle. The output value is determined by processing the infor- mation in the hidden layers and the output layer.
Figure 4 The structure of Feed-Forward Backpropagation Neural Network In this network structure, the information received from the in- puts is transmitted to the hidden layer and has a one-way working principle. The output value is determined by processing the infor- mation in the hidden layers and the output layer.
Figure 6 The structure of Cascade Forward Back-propagation Neural Network Cascade Forward Back-propagation Neural Networks are similar to feed-forward networks. The difference is that the data from the input contains a link to each hidden layer.
Figure 6 The structure of Cascade Forward Back-propagation Neural Network Cascade Forward Back-propagation Neural Networks are similar to feed-forward networks. The difference is that the data from the input contains a link to each hidden layer.
Figure 7 Hyperbolic Tangent Sigmoid Activation Function The input-output relationship of the hyperbolic tangent sigmoid transfer function is demonstrated in Fig. 7, where n is the input value and a is the output value for this activation function.
Figure 7 Hyperbolic Tangent Sigmoid Activation Function The input-output relationship of the hyperbolic tangent sigmoid transfer function is demonstrated in Fig. 7, where n is the input value and a is the output value for this activation function.
Figure 9 Satlins Activation Function. The Satlins function is an inverse Z-shaped activation function that transmits to the output in the space interval [-1 1], gives an output of —1 for values between —1 and infinity, and gives an output of 1 for values between 1 and infinity. This function is mathematically expressed as follows:
Figure 9 Satlins Activation Function. The Satlins function is an inverse Z-shaped activation function that transmits to the output in the space interval [-1 1], gives an output of —1 for values between —1 and infinity, and gives an output of 1 for values between 1 and infinity. This function is mathematically expressed as follows:
© Table 1 Training results on modeling the Rucklidge chaotic system with different ANN structures
© Table 1 Training results on modeling the Rucklidge chaotic system with different ANN structures
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