# Synchronization and Application of a Novel Hyperchaotic System Based on Adaptive Observers
## 3 Circuit Implementation of the Proposed Hyperchaotic System  
Using Multisim 14.3 software, an analogous electronic circuit for the novel hyperchaotic system was created in order to evaluate the viability of the proposed system. The highly visual modeling environment offered by the electronic circuit simulation program Multisim is designed for hyperchaotic systems [34]. It makes the process of creating and fine-tuning circuit models easier and permits the monitoring of their behavior in real time. This real-time feedback forms the basis for simulating the implementation of hyperchaotic systems in embedded circuitry and helps to understand their dynamic features. For simulating electronic circuits, a variety of software packages are available, including PSPICE 9.2, LTSPICE 17.1.15, Multisim 14.3 and Matlab Simulink 2021a. Multisim, the industry-standard circuit design and simulation program for analog, digital and power electronics in academic and research settings, was chosen for this thesis [35]. An operational amplifier (TL084 ACN), a multiplier (IC AD633), linear resistors and capacitors driven by a \(\pm\)15 V power source are all included in the developed circuit in this thesis. The operational amplifier adds, subtracts and integrates the circuits, and the multiplier, which combines the four state variables into a single cohesive unit, symbolizes the nonlinearity of the system. The system (1) presents the hyperchaotic system from which the electrical circuit equations are obtained, and (9) formulates it:\[ \begin{split}\dot{x}_{1}&=\frac{1}{C_{1}}\Big{[}\frac{1}{R_{1 }}x_{1}+\frac{1}{R_{2}}\Big{(}\frac{R_{9}}{R_{8}}\Big{)}(-x_{2})\Big{]}\\ \dot{x}_{2}&=\frac{1}{C_{2}}\Big{[}\frac{1}{R_{10}} \Big{(}\frac{R_{4}}{R_{3}}\Big{)}(-x_{1})+\frac{1}{R_{6}}x_{2}+\frac{1}{R_{7}} \frac{x_{1}x_{3}}{10}\Big{]}\\ \dot{x}_{3}&=\frac{1}{C_{3}}\Big{[}\frac{1}{R_{14}} \Big{(}\frac{R_{9}}{R_{8}}\Big{)}(-x_{2})+\frac{1}{R_{12}}\Big{(}\frac{R_{4}} {R_{3}}\Big{)}\frac{(-x_{1})x_{2}}{10}+\frac{1}{R_{11}}x_{3}+\frac{1}{R_{17}} \Big{(}\frac{R_{16}}{R_{15}}\Big{)}(-x_{4})\Big{]}\\ \dot{x}_{4}&=\frac{1}{C_{4}}\Big{[}\frac{1}{R_{20}}x _{1}+\frac{1}{R_{13}}\Big{(}\frac{R_{4}}{R_{3}}\Big{)}\frac{(-x_{1})x_{2}}{10 }+\frac{1}{R_{5}}x_{4}\Big{]}\end{split}  \tag{9}\]  
After performing the necessary calculations, the values of the circuit elements were determined as follows: \(R_{1}=0.833\)\(\mathrm{k}\Omega\), \(R_{2}=0.333\)\(\mathrm{k}\Omega\), \(R_{3}=R_{4}=R_{8}=R_{9}=R_{15}=R_{16}=100\)\(\mathrm{k}\Omega\), \(R_{5}=5\)\(\mathrm{k}\Omega\), \(R_{6}=R_{11}=R_{17}=10\)\(\mathrm{k}\Omega\), \(R_{7}=R_{12}=R_{13}=1\)\(\mathrm{k}\Omega\), \(R_{10}=R_{20}=0.222\)\(\mathrm{k}\Omega\), \(R_{14}=0.666\)\(\mathrm{k}\Omega\) and \(C_{1}=C_{2}=C_{3}=C_{4}=100\)\(\mathrm{\SIUnitSymbolMicro}\). The Multisim model of the circuit is illustrated in Figure 9. The circuit model encompasses seven operational amplifiers (TL084 ACN), four capacitors, three multipliers (IC AD633), and eighteen resistors. Figure 9: Electronic circuit diagram of the proposed hyperchaotic system. When the circuit simulation is run, the oscilloscope images showing the phase diagrams of the states are as shown in Figure 10.  
Similarity was observed between the graphs obtained from the numerical simulation program MATLAB 2021a and the electronic circuit simulation software. Multisim provides a strong confirmation for hyperchaotic attractors. Thoroughly comparing the output data from both software tools shows that there is a significant degree of consistency in the way attractors dynamically behave under different settings and how easily they alter. These results validate the presence of attractors in the hypothesized hyperchaotic system. Finally, consistency between the electrical circuit simulation findings and numerical simulation results provides a solid theoretical foundation for the actual implementation of the novel hyperchaotic system, while also confirming the feasibility of the system.