*A Collection of Papers on Chaos Theory and Its Applications*

$$\begin{cases} \dot{\mathbf{x}}\_1 = \mathbf{x}\_2 - \mathbf{x}\_1 \\\\ \dot{\mathbf{x}}\_2 = \mathbf{x}\_3 \\\\ \dot{\mathbf{x}}\_3 = \mathbf{x}\_4 \\\\ \dot{\mathbf{x}}\_4 = -\mathbf{x}\_4 - f(\mathbf{x}\_3) - 5\mathbf{x}\_2 - 0.125\mathbf{x}\_1 \end{cases} \tag{4}$$

**Figure 3.** *The corresponding circuit schematic diagram of Eq. (4).*

**Figure 4.** *Numerical and actual circuit state space plot in x*<sup>2</sup> � *x*<sup>3</sup> *plane and x*<sup>3</sup> � *x*<sup>4</sup> *plane.*

*Chaotic Systems with Hyperbolic Sine Nonlinearity DOI: http://dx.doi.org/10.5772/intechopen.94518*

**Figure 5.** *The corresponding circuit schematic diagram of Eq. (5).*

**Figure 6.** *Numerical and actual circuit state space plot in x*<sup>1</sup> *x*<sup>5</sup> *plane and x*<sup>2</sup> *x*<sup>3</sup> *plane.*

The corresponding circuit schematic diagram of Eq. (4) is shown as **Figure 3**. Its numerical and actual circuit state space plot is shown as **Figure 4**. When n = 5, the equations of fifth-order chaotic systems will be:

$$\begin{cases} \dot{\mathbf{x}}\_1 = \mathbf{x}\_2 - \mathbf{x}\_1 \\\\ \dot{\mathbf{x}}\_2 = \mathbf{x}\_3 - \mathbf{x}\_2 \\\\ \dot{\mathbf{x}}\_3 = \mathbf{x}\_4 \\\\ \dot{\mathbf{x}}\_4 = \mathbf{x}\_5 \\\\ \dot{\mathbf{x}}\_5 = -\mathbf{x}\_5 - f(\mathbf{x}\_4) - \mathbf{5}\mathbf{x}\_3 - \mathbf{5}\mathbf{x}\_2 - \mathbf{0}.\mathbf{1}\mathbf{x}\_1 \end{cases} \tag{5}$$

The corresponding circuit schematic diagram of Eq. (5) is shown as **Figure 5**. Its numerical and actual circuit state space plot is shown as **Figure 6**.
