# Control of the modified chaotic Chua's circuit using threshold method

## Keywords:

chaos, Chua, control, threshold method## Abstract

**Introduction**. General scientific fields where can be used circuits that realize chaotic behavior and generate chaotic oscillations are presented.Methods for control of chaotic oscillations are also presented. For modelling, analysis and demonstrate results was selected MultiSim software environment.

**Modelling and Analysis of Non-Linear Element**. This modified Chua’s circuit has a simple non-linear element, designed to have a piecewise-linear characteristic, that is, a combination of an opamp with two diodes that are mutually inline. For realization of nonlinearity, for two diodes do not need a separate power source, only one bipolar power source for the opamp is enough. The scheme for modelling of the nonlinear element and the results of computer simulation, i.e. the volt-ampere characteristic (VAC) at certain values of the components of the scheme's nominal values, is presented. This modified Chua's circuit, which generates a chaotic and controlled attractor with a fixed period, can be used in modern transmission and reception systems of information.

**Modeling and Analysis of the Modified Chaotic Chua’s Generator**. System’s behavior is investigated through numerical simulations, by using well known tools of nonlinear theory, such as chaotic attractor and time distributions of the chaotic coordinates.

**Threshold Method for Control of Chaotic Oscillations**. System of equations that realize chaotic oscillations of Chua's circuit is presented. Using threshold method was practical realization of the control of chaotic attractor. This modified Chua’scircuit that generate a chaotic and controlled attractor with a fixed period can be used in modern systemstransmitting and receiving information. Number of periodic (controlled) attractor can be used as a keys formasking of information carrier.

**Conclusions**. For the first time was used threshold method forcontrol of chaotic oscillations for modified Chua’schaotic generator. This modified Chua’s circuit thatgenerate a chaotic and controlled attractor with afixed period can be used in modern systems transmittingand receiving information. Number of periodic(controlled) attractor can be used as a keys for maskingof information carrier.

## References

Hajnova V. and Pribylova L. (2017) Two-parameter bifurcations in LPA model. *Journal of Mathematical Biology*, Vol. 75, Iss. 5, pp. 1235-1251. DOI: 10.1007/s00285-017-1115-8

Rusyn V. and Savko O. (2016) Modeling of Chaotic Behavior in the Economic Model. *Chaotic Modeling and Simulation. An International Journal of Nonlinear Science*, No. 3. pp. 291–298.

Pribylova L. (2009) Bifurcation routes to chaos in an extended Van der Pol’s equation applied to economic models *Electronic Journal of Differential Equations*, Vol. 53, pp. 1–21.

Bucur L. and Florea A. (2011) Techniques for prediction in chaos – a comparative study on financial data *U.P.B. Sci. Bull., Series C*, Vol. 73, No. 3., pp. 17-32.

Agop M., Dimitriu D.G., Niculescu O., Poll E. and Radu V. (2013) Experimental and theoretical evidence for the chaotic dynamics of complex structures. *Physica Scripta*, Vol. 87, Iss. 4, pp. 045501. DOI: 10.1088/0031-8949/87/04/045501

Horley P.P., Kushnir M.Y., Morales-Meza M., Sukhov A. and Rusyn V. (2016) Period-doubling bifurcation cascade observed in a ferromagnetic nanoparticle under the action of a spin-polarized current. *Physica B: Condensed Matter*, Vol. 486, pp. 60-63. DOI: 10.1016/j.physb.2015.12.010

Chua L. (1971) Memristor-The missing circuit element. *IEEE Transactions on Circuit Theory*, Vol. 18, Iss. 5, pp. 507-519. DOI: 10.1109/tct.1971.1083337

Wang F.Z., Shi L., Wu H., Helian N. and Chua L.O. (2017) Fractional memristor. *Applied Physics Letters*, Vol. 111, Iss. 24, pp. 243502. DOI: 10.1063/1.5000919

Ascoli A., Tetzlaff R., Biey M. and Chua L.O. (2017) Complex dynamics in circuits with memristors. *2017 European Conference on Circuit Theory and Design (ECCTD)*. DOI: 10.1109/ecctd.2017.8093268

Mannan Z.I., Choi H., Rajamani V., Kim H. and Chua L. (2017) Chua Corsage Memristor: Phase Portraits, Basin of Attraction, and Coexisting Pinched Hysteresis Loops. *International Journal of Bifurcation and Chaos*, Vol. 27, Iss. 03, pp. 1730011. DOI: 10.1142/s0218127417300117

Itoh M. and Chua L. (2017) Dynamics of Hamiltonian Systems and Memristor Circuits. *International Journal of Bifurcation and Chaos*, Vol. 27, Iss. 02, pp. 1730005. DOI: 10.1142/s0218127417300051

Yu D., Zheng C., Iu H.H., Fernando T. and Chua L.O. (2017) A New Circuit for Emulating Memristors Using Inductive Coupling. *IEEE Access*, Vol. 5, pp. 1284-1295. DOI: 10.1109/access.2017.2649573

Chua L. (2013) Memristor, Hodgkin–Huxley, and Edge of Chaos. *Nanotechnology*, Vol. 24, Iss. 38, pp. 383001. DOI: 10.1088/0957-4484/24/38/383001

Adhikari S.P., Kim H., Budhathoki R.K., Yang C. and Chua L.O. (2015) A Circuit-Based Learning Architecture for Multilayer Neural Networks With Memristor Bridge Synapses. *IEEE Transactions on Circuits and Systems I: Regular Papers*, Vol. 62, Iss. 1, pp. 215-223. DOI: 10.1109/tcsi.2014.2359717

Gregory M.D. and Werner D.H. (2015) Application of the Memristor in Reconfigurable Electromagnetic Devices. *IEEE Antennas and Propagation Magazine*, Vol. 57, Iss. 1, pp. 239-248. DOI: 10.1109/map.2015.2397153

Potrebic M. and Tosic D. (2015) Application of Memristors in Microwave Passive Circuits. *Radioengineering*, Vol. 24, Iss. 2, pp. 408-419. DOI: 10.13164/re.2015.0408

Khrapko S., Rusyn V. and Politansky L. (2018) Investigation of the memristor nonlinear properties. *Informatics Control Measurement in Economy and Environment Protection*, Vol. 8, Iss. 1, pp. 12-15. DOI: 10.5604/01.3001.0010.8544

Bao B., Yu J., Hu F. and Liu Z. (2014) Generalized Memristor Consisting of Diode Bridge with First Order Parallel RC Filter. *International Journal of Bifurcation and Chaos*, Vol. 24, Iss. 11, pp. 1450143. DOI: 10.1142/s0218127414501430

Valsa J., Biolek D. and Biolek Z. (2010) An analogue model of the memristor. *International Journal of Numerical Modelling: Electronic Networks, Devices and Fields*, Vol. 24, Iss. 4, pp. 400-408. DOI: 10.1002/jnm.786

Rusyn V. B. (2014) Modelling and Research of Chaotic Rossler System with LabView and Multisim Software Environment, *Visnyk NTUU KPI Seriia - Radiotekhnika Radioaparatobuduvannia*, Iss. 59, pp. 21-28. DOI: 10.20535/RADAP.2014.59.21-28

Sambas A., Mada Sanjaya W. S., Mamat M. and Tacha O. (2013) Design and Numerical Simulation of Unidirectional Chaotic Synchronization and Its Application in Secure Communication System. *Journal of Engineering Science and Technology Review*, Vol. 6, No. 4, pp. 66-73.

Ott E., Grebogi C. and Yorke J.A. (1990) Controlling chaos. *Physical Review Letters*, Vol. 64, Iss. 11, pp. 1196-1199. DOI: 10.1103/physrevlett.64.1196

Rusyn V., Kushnir M. and Galameiko O. (2012) Hyperchaotic Control by Thresholding Method. *Proceedings of International Conference on Modern Problem of Radio Engineering, Telecommunications and Computer Science*, p. 67.

Rusyn V.B., Stancu A. and Stoleriu L. (2015). Modeling and Control of Chaotic Multi-Scroll Jerk System in LabView. *Visnyk NTUU KPI Seriia - Radiotekhnika Radioaparatobuduvannia*, Iss. 63, pp. 94-99. DOI: 10.20535/RADAP.2015.63.94-99

Bai E. and Lonngren K.E. (1999) Synchronization and Control of Chaotic Systems. *Chaos, Solitons & Fractals*, Vol. 10, Iss. 9, pp. 1571-1575. DOI: 10.1016/s0960-0779(98)00204-5

Chen S. and Lü J. (2002) Synchronization of an uncertain unified chaotic system via adaptive control. *Chaos, Solitons & Fractals*, Vol. 14, Iss. 4, pp. 643-647. DOI: 10.1016/s0960-0779(02)00006-1

Bowong S. and Kakmeni F.M. (2004) Synchronization of uncertain chaotic systems via backstepping approach. *Chaos, Solitons & Fractals*, Vol. 21, Iss. 4, pp. 999-1011. DOI: 10.1016/j.chaos.2003.12.084

Gupte N. and Amritkar R.E. (1993) Synchronization of chaotic orbits: The influence of unstable periodic orbits. *Physical Review E*, Vol. 48, Iss. 3, pp. R1620-R1623. DOI: 10.1103/physreve.48.r1620

Dong W., Wang B., Long Y., Zhu D. and Sun S. (2017) Finite time control of nonlinear permanent magnet synchronous motor *U.P.B. Sci. Bull., Series C*, Vol. 79, No. 2, pp. 145-156.

Calofir V., Tanasa V., Fagarasan I., Stamatescu I., Arghira N. and Stamatescu G. (2015) A backstepping control method for a nonlinear process - two coupled-tanks *U.P.B. Sci. Bull., Series C*, Vol. 77, No. 3, pp. 67-76.

Murali K. and Sinha S. (2003) Experimental realization of chaos control by thresholding. *Physical Review E*, Vol. 68, Iss. 1. DOI: 10.1103/physreve.68.016210

## Downloads

## Published

## How to Cite

*Visnyk NTUU KPI Seriia - Radiotekhnika Radioaparatobuduvannia*, 0(75), pp. 61-65. Available at: https://radap.kpi.ua/radiotechnique/article/view/1511 (Accessed: 16September2024).

## Issue

## Section

## License

Authors who publish with this journal agree to the following terms:

- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).