# Hybrid Analog Computer for Modeling Nonlinear Dynamical Systems: The Complete Cookbook

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## Abstract

**:**

## 1. Introduction

## 2. Brief Overview of the Systematic Design of Lumped Chaotic Oscillators

## 3. Construction of a Hybrid Computer

#### 3.1. Integrators and ’Summators’

#### 3.2. Multipliers and Counting-Based Potentiometers

#### 3.3. Inverters, Amplifiers, Constant Sources

#### 3.4. Digitally Controlled Components

## 4. Simulations with Hybrid Computers

- Obtaining a mathematical description of the problem to be solved;
- Decomposition of the mathematical description into a set of operations available on the used device;
- The transformation of variables involving a limited range of used devices, i.e., the range of a machine unit;
- Time-variable transformation;
- Creating and wiring programming schema.

#### 4.1. Simulation of a Simple Nonlinear Chaotic System

#### 4.2. Hybrid Analog Computer in Sensor Applications

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Programming schema according to Equation (11).

**Figure 7.**Simulated state attractors of the system ${\mathrm{JD}}_{0}$ (11) by MATLAB; (

**a**) [$x,px$], (

**b**) [$x,{p}^{2}x$], (

**c**) [$px,{p}^{2}x$].

**Figure 8.**Measured state attractors of the system ${\mathrm{JD}}_{0}$ (12) by the proposed hybrid computer; (

**a**) [$x,px$], (

**b**) [$x,{p}^{2}x$], (

**c**) [$px,{p}^{2}x$].

**Figure 9.**Recurrence plot for the measured chaotic waveform: (

**a**) $x\left(t\right)$, (

**b**) $dx\left(t\right)/dt$, and (

**c**) ${d}^{2}x/d{t}^{2}$. Subplot (

**d**) gives the normalized frequency spectrum of the measured waveforms.

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**MDPI and ACS Style**

Rujzl, M.; Polak, L.; Petrzela, J.
Hybrid Analog Computer for Modeling Nonlinear Dynamical Systems: The Complete Cookbook. *Sensors* **2023**, *23*, 3599.
https://doi.org/10.3390/s23073599

**AMA Style**

Rujzl M, Polak L, Petrzela J.
Hybrid Analog Computer for Modeling Nonlinear Dynamical Systems: The Complete Cookbook. *Sensors*. 2023; 23(7):3599.
https://doi.org/10.3390/s23073599

**Chicago/Turabian Style**

Rujzl, Miroslav, Ladislav Polak, and Jiri Petrzela.
2023. "Hybrid Analog Computer for Modeling Nonlinear Dynamical Systems: The Complete Cookbook" *Sensors* 23, no. 7: 3599.
https://doi.org/10.3390/s23073599