students learning and teaching efficacy can be increased by about 20% percent for the solved case study in Matlab software compared to conventional teaching and learning systems.

## 9. Conclusions

This article is a review of applications of the two-dimensional piece-wise linear chaotic Lozi map developed over the four last decades. These applications concern many areas (cryptography, electronic devices, memristors, optimization, synchronization, secure communications, AI with swarm intelligence, chimeras, solitary states, and more). As new applications have been regularly discovered at an accelerated pace over the last decade, there was a need to render them more easily accessible, which is the goal of this survey.

The Lozi map was initially discovered in the limited context of chaotic dynamical systems as they existed in the 1970s, when it was used as a toy model to rigorously prove the existence of a strange (and chaotic) attractor for plane mapping, which seemed inaccessible for the Hénon map. When I first began to study this model in June 1977, (without, of course all of the modern mathematical tools developed since then), I was convinced that a few weeks would be enough to explain the structure of such an attractor, as it was basically composed of line segments. However, the task turned out to be more difficult than I expected, mainly because unlike Michal Misiurewicz, I did not limit the range of the parameter values for the study. Following Misiurewicz's work, hundreds of papers were published on countless aspects of this chaotic attractor.

Today, if we go back to the late 1970s, life was very different from now in many ways. There were no personal computers (Michel Hénon used one of the only two computers at the University of Nice, an IBM 7040, to plot the figure of his original paper), no internet, and no mobile phones. Communications between researchers took place through slow post office mail and air travel was very expensive, limiting in-person contact between researchers. Technological advancements over the past fifty years have been spectacular in all aspects of life. It took almost my entire professional life as a mathematician to see the results I expected to be published in a few weeks.

However, amazingly, I was able to see the great unity of mathematics over these decades. For example, since 1975, when I was a young associate professor, I have been dis-appointed for years in the search for a classical global optimization algorithm able to avoid pseudo-minima. It is funny to notice how the map I introduced for a completely different purpose is now commonly used to solve this problem through a metaheuristic algorithms.

Thus, it is difficult to predict what the next areas of application of this map will be in the future. Perhaps in the field of biological and medical sciences, where research using chaos seems promising? Perhaps more advances are coming in control theory and cryptography? It can be observed that the Lozi map belongs to the class of chaotic and hyperchaotic systems which possess Input-to-State Stability (ISS)-like features. These systems are now involved in this field (see [167]).

With new applications being regularly discovered at an accelerated pace over the past decade, there is no reason to think that this phenomenon will stop.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The author declares no conflict of interest.

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41. Al-Saidi, N.M.G.; Natiq, H.; Baleanu, D.; Ibrahim, R.W. The dynamic and discrete systems of variable fractional order in the sense of the Lozi structure map. *AIMS Math.* **2023**, *8*, 733–751. [CrossRef]

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7. Lozi, R. Analyse Numérique de Certains Problèmes de Bifurcation, Ph.D. Thesis, University of Nice, Nice, France, 1975.

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9. Lozi, R. Un attracteur étrange (?) du type attracteur de Hénon. *J. Phys.* **1978**, *39*, C5-9-C5-10. [CrossRef]

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25. Ishii, Y. Towards a kneading theory for Lozi mappings II: Monotonicity of the Topological Entropy and Hausdorff Dimension of Attractors. Commun. Math. Phys. **1997**, *190*, 375-394. [CrossRef]

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34. Zhusubaliyev, Z.T.; Mosekilde, E. Multistability and hidden attractors in a multilevel DC/DC converter. *Math. Comput. Simul.* **2015**, *109*, 32-45. [CrossRef]

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36. Zhang, L.-P.; Liu, Y.; Wei, Z.-C.; Jiang, H.-B.; Bi, Q.-S. A novel class of two-dimensional chaotic maps with infinitely many coexisting attractors. *Chin. Phys. B* **2020**, *29*, 060501. [CrossRef]

37. Bao, H.; Hua, Z.Y.; Wang, N.; Zhu, L.; Chen, M.; Bao, B.C. Initials-boosted coexisting chaos in a 2D Sine map and its hardware implementation. *IEEE Trans. Ind. Inform.* **2021**, *17*, 1132-1140. [CrossRef]

38. Li, B.; Gu, E.-G. The stratification and invariant region in the sea of an area-preserving map. *Res. Sq.* **2023**, preprint. [CrossRef]

39. Khennaoui, A.-A.; Ouannas, A.; Bendoukha, S.; Grassi, G.; Lozi, R.; Pham, V.-T. On fractional-order discrete-time systems: Chaos, stabilization and synchronization. *Chaos Solitons Fractals* **2019**, *119*, 150-162. [CrossRef]

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42. Joshi, D.D.; Gade, P.M.; Bhalekar, S. Study of low-dimensional nonlinear fractional difference equations of complex order. *Chaos* **2022**, *32*, 113101. [CrossRef] [PubMed]
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47. Chua, L.O. Memristor-the missing circuit element. *IEEE Trans. Circuit Theory* **1971**, *18*, 507–519. [CrossRef]

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88. Coelho, L.d.S.; Maidl, G.; Pierezan, J.; Mariani, V.C.; da Luz, M.V.F.; Leite, J.V. Ant Lion Approach Based on Lozi Map for Multiobjective Transformer Design Optimization. In *Proceedings of the International Symposium on Power Electronics, Electrical Drives, Automation and Motion (SPEEDAM)*, Amalfi, Italy, 20–22 June 2018; pp. 280–285. [CrossRef]

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118. Chen, G.; Chen, Y.; Ogmen, H. Identifying chaotic systems via a Wiener-type cascade models. *IEEE Control Syst.* **1997**, *17*, 29–36. [CrossRef]

119. Xu, M.; Chen, G.; Tian, Y.-G. Identifying chaotic systems using Wiener and Hammerstein cascade models. *Math. Comput. Model.* **2001**, *33*, 483–493. [CrossRef]

120. Sira-Ramirez, H.; Ibanez, C.A.; Suarez-Castagnon, M. Exact state reconstructors in the recovery of messages encrypted by the sates of nonlinear discrete-time chaotic systems. *Int. J. Bifurc. Chaos* **2004**, *12*, 169–177. [CrossRef]

121. Aliwi, B.H.; Ajeena, R.K.K. A performed knapsack problem on the fuzzy chaos cryptosystem with cosine Lozi chaotic map. *AIP Conf. Proc.* **2023**, *2414*, 040047.

122. Alawida, M.; Samsudin, A.; Teh, J.S.; Alshoura, W.H. Digital Cosine Chaotic Map for Cryptographic Applications. *IEEE Access* **2019**, *7*, 150609–150622. [CrossRef]

123. Su, Y.; Xu, W.; Li, T.; Zhao, J.; Liu, S. Optical color image encryption based on fingerprint key and phase-shifting digital holography. *Optics Lasers Eng.* **2021**, *140*, 106550. [CrossRef]

124. Wang, Y.; Zhao, Q.; Zhang, H.; Li, T.; Xu, W.; Liu, S.; Su, Y. Optical single-channel color image encryption based on chaotic fingerprint phase mask and diffractive imaging. *Appl. Opt.* **2023**, *62*, 1009–1018. [CrossRef] [PubMed]

125. Suresh, D.K.; MadhaviLatha, M.; Singh, M.K. Image authentication with tampering localization using chaotic and neural mapping. *Int. J. Neural Netw. Adv. Appl.* **2014**, *1*, 20–29. Available online: https://www.naun.org/cms.action?id=7634 (accessed on 23 August 2023).

126. Cicek, S. Microcontroller-based random number generator implementation by using discrete chaotic maps. *Sak. Univ. J. Sci.* **2020**, *24*, 832–844. [CrossRef]

127. Merah, L.; Ali-Pacha, A.; Hadj-Said, N.; Mecheri, B.; Dellassi, M. FPGA hardware co-simulation of new chaos-based stream cipher based on Lozi Map. *Int. J. Eng. Technol.* **2017**, *9*, 420–425. [CrossRef]

128. Xiao, Y.; Wang, Z.; Cao, J.; Deng, R.; Liu, Y.; He, J.; Chen, L. Time-frequency domain encryption with SLM scheme for physical-layer security in an OFDM-PON system. *J. Opt. Commun. Netw.* **2018**, *10*, 46–51. [CrossRef]

129. Pecora, L.M.; Carroll, T.L. Synchronization in chaotic systems. *Phys. Rev. Lett.* **1990**, *64*, 821–824. [CrossRef]

130. Zhang, H.; Li, C.; Liao, X. Observer-based synchronization for piecewise-linear discrete chaotic systems based on piecewise quadratic Lyapunov functions. *Int. J. Bifurc. Chaos* **2005**, *19*, 4389–4397. [CrossRef]

131. Angeli, A.; De Genesio, R.; Tesi, A. Deadbeat chaos synchronization in discrete-time systems. *IEEE Trans. Circuits Syst.* **1995**, *42*, 54–56. [CrossRef]

132. Grassi, G. Propagation of projectives synchronization in a series connection of chaotic systems. *J. Frankl. Inst.* **2010**, *347*, 438–451. [CrossRef]

133. Devaney, R.L. A piecewise linear model for the zones of instability of an area-preserving map. *Physica D* **1984**, *10*, 387–393. [CrossRef]

134. Lian K.-Y.; Liu, P. Chiu, C.-S.; Chiang, T.-S. Robust Dead-beat synchronization and communication for discrete-time chaotic systems. *Int. J. Bifurc. Chaos* **2002**, *12*, 835–846. [CrossRef]

135. Zheng, Y.-A.; Nian, Y.-B.; Liu, Z.-R. Impulsive synchronization of Discrete chaotic systems. *Chin. Phys. Lett.* **2003**, *20*, 199–201. [CrossRef]

136. Zhang, L.; Jiang, H. Impulsive generalized synchronization for a class of nonlinear discrete chaotic systems. *Commun. Nonlinear Sci. Numer. Simulat.* **2011**, *16*, 2027–2032. [CrossRef]

137. Vasegh, N.; Majd, V.J. Adaptive fuzzy synchronization of discrete-time chaotic systems. *Chaos Solitons Fractals* **2006**, *28*, 1029–1036. [CrossRef]

138. Dmitriev, A.S.; Kassian, G.A.; Khilinsky, A.D.; Hasler, M. Chaotic Synchronization Via Minimum Information Transmission. *arXiv* **2002**, arXiv:nlin/0205029. [CrossRef]

139. Coelho, L.S.; de Andrade Bernert, D.L. PID control design for chaotic synchronization using a tribes optimization approach. *Chaos Solitons Fractals* **2009**, *42*, 634–640. [CrossRef]

140. Clerc, M. *Particle Swarm Optimization*; ISTE: London, UK, 2006.

141. Roy, B.; Acharyya, A.B. Synchronization of globally coupled Lozi map using periodically varying parameter. *Acta Phys. Pol. B* **2019**, *50*, 1671–1679. [CrossRef]

142. Cano, A.V.; Cosenza, M.G. Chimeras and clusters in networks of hyperbolic chaotic oscillators. *Phys. Rev. E* **2017**, *95*, 030202(R). [CrossRef]

143. Parastesh, F.; Jafari, S.; Azarnoush, H.; Shahriari, Z.; Wang, Z.; Boccaletti, S.; Perc, M. Chimeras. *Phys. Rep.* **2021**, *898*, 1–114. [CrossRef]

144. Semenova, N.; Zakharova, A.; Schöll, E.; Anishchenko, V. Impact of hyperbolicity on chimera states in ensembles of nonlocally coupled chaotic oscillators. *AIP Conf. Proc.* **2016**, *1738*, 210014. [CrossRef]

145. Semenova, N.; Zakharova, A.; Schöll, E.; Anishchenko, V. Does hyperbolicity impede emergence of chimera states in networks of nonlocally coupled chaotic oscillators? *Europhys. Lett.* **2015**, *112*, 40002. [CrossRef]

146. Anishchenko, V.; Rybalova, E.; Semenova, N. Chimera States in two coupled ensembles of Henon and Lozi maps. *Controlling chimera states*. *AIP Conf. Proc.* **2018**, *1978*, 470013. [CrossRef]
117. Feng, G.; Chen, G. Adaptive control of discrete-time chaotic systems: A fuzzy control approach. *Chaos Solitons Fractals* **2005**, *23*, 459–467. [CrossRef]

118. Chen, G.; Chen, Y.; Ogmen, H. Identifying chaotic systems via a Wiener-type cascade models. *IEEE Control Syst.* **1997**, *17*, 29–36. [CrossRef]

119. Xu, M.; Chen, G.; Tian, Y.-G. Identifying chaotic systems using Wiener and Hammerstein cascade models. *Math. Comput. Model.* **2001**, *33*, 483–493. [CrossRef]

120. Sira-Ramirez, H.; Ibanez, C.A.; Suarez-Castagnon, M. Exact state reconstructors in the recovery of messages encrypted by the sates of nonlinear discrete-time chaotic systems. *Int. J. Bifurc. Chaos* **2004**, *12*, 169–177. [CrossRef]

121. Aliwi, B.H.; Ajeena, R.K.K. A performed knapsack problem on the fuzzy chaos cryptosystem with cosine Lozi chaotic map. *AIP Conf. Proc.* **2023**, *2414*, 040047.

122. Alawida, M.; Samsudin, A.; Teh, J.S.; Alshoura, W.H. Digital Cosine Chaotic Map for Cryptographic Applications. *IEEE Access* **2019**, *7*, 150609–150622. [CrossRef]

123. Su, Y.; Xu, W.; Li, T.; Zhao, J.; Liu, S. Optical color image encryption based on fingerprint key and phase-shifting digital holography. *Optics Lasers Eng.* **2021**, *140*, 106550. [CrossRef]

124. Wang, Y.; Zhao, Q.; Zhang, H.; Li, T.; Xu, W.; Liu, S.; Su, Y. Optical single-channel color image encryption based on chaotic fingerprint phase mask and diffractive imaging. *Appl. Opt.* **2023**, *62*, 1009–1018. [CrossRef] [PubMed]

125. Suresh, D.K.; MadhaviLatha, M.; Singh, M.K. Image authentication with tampering localization using chaotic and neural mapping. *Int. J. Neural Netw. Adv. Appl.* **2014**, *1*, 20–29. Available online: https://www.naun.org/cms.action?id=7634 (accessed on 23 August 2023).

126. Cicek, S. Microcontroller-based random number generator implementation by using discrete chaotic maps. *Sak. Univ. J. Sci.* **2020**, *24*, 832–844. [CrossRef]

127. Merah, L.; Ali-Pacha, A.; Hadj-Said, N.; Mecheri, B.; Dellassi, M. FPGA hardware co-simulation of new chaos-based stream cipher based on Lozi Map. *Int. J. Eng. Technol.* **2017**, *9*, 420–425. [CrossRef]

128. Xiao, Y.; Wang, Z.; Cao, J.; Deng, R.; Liu, Y.; He, J.; Chen, L. Time-frequency domain encryption with SLM scheme for physical-layer security in an OFDM-PON system. *J. Opt. Commun. Netw.* **2018**, *10*, 46–51. [CrossRef]

129. Pecora, L.M.; Carroll, T.L. Synchronization in chaotic systems. *Phys. Rev. Lett.* **1990**, *64*, 821–824. [CrossRef]

130. Zhang, H.; Li, C.; Liao, X. Observer-based synchronization for piecewise-linear discrete chaotic systems based on piecewise quadratic Lyapunov functions. *Int. J. Bifurc. Chaos* **2005**, *19*, 4389–4397. [CrossRef]

131. Angeli, A.; De Genesio, R.; Tesi, A. Deadbeat chaos synchronization in discrete-time systems. *IEEE Trans. Circuits Syst.* **1995**, *42*, 54–56. [CrossRef]

132. Grassi, G. Propagation of projectives synchronization in a series connection of chaotic systems. *J. Frankl. Inst.* **2010**, *347*, 438–451. [CrossRef]

133. Devaney, R.L. A piecewise linear model for the zones of instability of an area-preserving map. *Physica D* **1984**, *10*, 387–393. [CrossRef]

134. Lian K.-Y.; Liu, P. Chiu, C.-S.; Chiang, T.-S. Robust Dead-beat synchronization and communication for discrete-time chaotic systems. *Int. J. Bifurc. Chaos* **2002**, *12*, 835–846. [CrossRef]

135. Zheng, Y.-A.; Nian, Y.-B.; Liu, Z.-R. Impulsive synchronization of Discrete chaotic systems. *Chin. Phys. Lett.* **2003**, *20*, 199–201. [CrossRef]

136. Zhang, L.; Jiang, H. Impulsive generalized synchronization for a class of nonlinear discrete chaotic systems. *Commun. Nonlinear Sci. Numer. Simulat.* **2011**, *16*, 2027–2032. [CrossRef]

137. Vasegh, N.; Majd, V.J. Adaptive fuzzy synchronization of discrete-time chaotic systems. *Chaos Solitons Fractals* **2006**, *28*, 1029–1036. [CrossRef]

138. Dmitriev, A.S.; Kassian, G.A.; Khilinsky, A.D.; Hasler, M. Chaotic Synchronization Via Minimum Information Transmission. *arXiv* **2002**, arXiv:nlin/0205029. [CrossRef]

139. Coelho, L.S.; de Andrade Bernert, D.L. PID control design for chaotic synchronization using a tribes optimization approach. *Chaos Solitons Fractals* **2009**, *42*, 634–640. [CrossRef]

140. Clerc, M. *Particle Swarm Optimization*; ISTE: London, UK, 2006.

141. Roy, B.; Acharyya, A.B. Synchronization of globally coupled Lozi map using periodically varying parameter. *Acta Phys. Pol. B* **2019**, *50*, 1671–1679. [CrossRef]

142. Cano, A.V.; Cosenza, M.G. Chimeras and clusters in networks of hyperbolic chaotic oscillators. *Phys. Rev. E* **2017**, *95*, 030202(R). [CrossRef]

143. Parastesh, F.; Jafari, S.; Azarnoush, H.; Shahriari, Z.; Wang, Z.; Boccaletti, S.; Perc, M. Chimeras. *Phys. Rep.* **2021**, *898*, 1–114. [CrossRef]

144. Semenova, N.; Zakharova, A.; Schöll, E.; Anishchenko, V. Impact of hyperbolicity on chimera states in ensembles of nonlocally coupled chaotic oscillators. *AIP Conf. Proc.* **2016**, *1738*, 210014. [CrossRef]

145. Semenova, N.; Zakharova, A.; Schöll, E.; Anishchenko, V. Does hyperbolicity impede emergence of chimera states in networks of nonlocally coupled chaotic oscillators? *Europhys. Lett.* **2015**, *112*, 40002. [CrossRef]

146. Anishchenko, V.; Rybalova, E.; Semenova, N. Chimera States in two coupled ensembles of Henon and Lozi maps. *Controlling chimera states*. *AIP Conf. Proc.* **2018**, *1978*, 470013. [CrossRef]
147. Semenova, N.; Vadivasova, T.; Anishchenko, V. Mechanism of solitary state appearance in an ensemble of nonlocally coupled Lozi maps. *Eur. Phys. J. Spec. Top.* **2018**, *227*, 1173–1183. [CrossRef]

148. Rybalova, E.; Strelkova, G. Response of solitary states to noise-modulated parameters in nonlocally coupled networks of Lozi maps. *Chaos* **2022**, *32*, 021101. [CrossRef] [PubMed]

149. Rybalova, E.; Semenova, N.; Anishchenko, V. Solitary State Chimera: Appearance, Structure, and Synchronization. In Proceedings of the 2018 International Symposium on Nonlinear Theory and Its Applications NOLTA2018, Tarragona, Spain, 2–6 September 2018; pp. 601–604.

150. Bukh, A.; Rybalova, E.; Semenova, N.; Strelkova, G.; Anishchenko, V. New type of chimera and mutual synchronization of spatiotemporal structures in two coupled ensembles of nonlocally interacting chaotic maps. *Chaos* **2017**, *27*, 111102. [CrossRef]

151. Rybalova, E.; Strelkova, G.; Schöll, E.; Anishchenko, V. Relay and complete synchronization in heterogeneous multiplex networks of chaotic maps. *Chaos* **2020**, *30*, 061104. [CrossRef]

152. Rybalova, E.; Strelkova, G.; Anishchenko, V. Mechanism of realizing a solitary state chimera in a ring of nonlocally coupled chaotic maps. *Chaos Solitons Fractals* **2018**, *115*, 300–305. [CrossRef]

153. Rybalova, E.; Schöll, E.; Strelkova, G. Controlling chimera and solitary states by additive noise in networks of chaotic maps. *J. Differ. Appl.* **2022**, 1–22. [CrossRef]

154. Chua, L.O.; Yang, L. Cellular neural networks: Theory. *IEEE Trans. Circuits Syst.* **1998**, *35*, 1257–1272. [CrossRef]

155. Chua, L.O.; Yang, L. Cellular neural networks: Applications. *IEEE Trans. Circuits Syst.* **1998**, *35*, 1273–1290. [CrossRef]

156. Chang, H.-M.; Juang, J. Piecewise two-dimensional maps and applications to cellular neural networks. *Int. J. Bifurc. Chaos* **2004**, *14*, 2223–2228. [CrossRef]

157. Chang, H.-M.; Juang, J. Boundary Influence on the Entropy of a Problem in Cellular Neural Networks. Master's Thesis, National Chiao Tung University, Taiwan, China, 2004. Available online: https://ir.nctu.edu.tw/bitstream/11536/52224/3/250303.pdf (accessed on 22 September 2023). (In English)

158. Skrynnyk, I.; Dmitrishin, D.; Stokolos, A.; Iacob, I.E. Computational aspects of large-length cycle search algorithms for nonlinear discrete systems. *Proc. Odessa Polytech. Univ.* **2019**, *58*, 69–84. Available online: http://dspace.opu.ua/jspui/handle/123456789/10522 (accessed on 28 July 2023). [CrossRef]

159. Shang, D.; Shang, P.; Liu, L. Multidimensional scaling method for complex time series feature classification based on generalized complexity-invariant distance. *Nonlinear Dyn.* **2019**, *95*, 2875–2892. [CrossRef]

160. Jacob, R.; Harikrishnan, K.P.; Misra, R.; Ambika, G. Measure for degree heterogeneity in complex networks and its application to recurrence network analysis. *R. Soc. Open Sci.* **2017**, *4*, 160757. [CrossRef]

161. Amigo, J.M.; Kennel, M.B. Topological permutation entropy. *Physica D* **2007**, *231*, 137–142. [CrossRef]

162. Mekler, A. Calculation of EEG correlation dimension: Large massifs of experimental data. *Comput. Methods Programs Biomed.* **2008**, *92*, 154–160. [CrossRef]

163. Yang, Y.; Duan, Z. An effective co-evolutionary algorithm based on artificial bee colony and differential evolution for time series predicting optimization. *Complex Intell. Syst.* **2020**, *6*, 299–308. [CrossRef]

164. Tang, T.W.; Allison, A.; Abbott, D. Investigation of chaotic switching strategies in Parrondo's games. *Fluct. Noise Lett.* **2004**, *4*, L585–L596. [CrossRef]

165. Harmer, G.P.; Abbott, D.; Taylor, P.G.; Parrondo, J.M.R. Brownian ratchets and Parrondo's games. *Chaos* **2001**, *11*, 705–714. [CrossRef] [PubMed]

166. Al-Hilli, W.H. Using Software's and Technology in Solving Mathematics Problem to Motivate and Accelerate the Learning Process. *EURASIA J. Math. Sci. Technol. Educ.* **2019**, *15*, em1670. [CrossRef] [PubMed]

167. Rodrigues, V. H. P.; Oliveira, T. R.; Cunha, J.P.V.S. Globally Stable Synchronization of Chaotic Systems Based on Norm Observers Connected in Cascade. *IEEE Trans. Circuits Syst. II Express Briefs* **2016**, *63*, 883–887. [CrossRef]

**Disclaimer/Publisher's Note:** The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
147. Semenova, N.; Vadivasova, T.; Anishchenko, V. Mechanism of solitary state appearance in an ensemble of nonlocally coupled Lozi maps. *Eur. Phys. J. Spec. Top.* **2018**, *227*, 1173–1183. [CrossRef]

148. Rybalova, E.; Strelkova, G. Response of solitary states to noise-modulated parameters in nonlocally coupled networks of Lozi maps. *Chaos* **2022**, *32*, 021101. [CrossRef] [PubMed]

149. Rybalova, E.; Semenova, N.; Anishchenko, V. Solitary State Chimera: Appearance, Structure, and Synchronization. In Proceedings of the 2018 International Symposium on Nonlinear Theory and Its Applications NOLTA2018, Tarragona, Spain, 2–6 September 2018; pp. 601–604.

150. Bukh, A.; Rybalova, E.; Semenova, N.; Strelkova, G.; Anishchenko, V. New type of chimera and mutual synchronization of spatiotemporal structures in two coupled ensembles of nonlocally interacting chaotic maps. *Chaos* **2017**, *27*, 111102. [CrossRef]

151. Rybalova, E.; Strelkova, G.; Schöll, E.; Anishchenko, V. Relay and complete synchronization in heterogeneous multiplex networks of chaotic maps. *Chaos* **2020**, *30*, 061104. [CrossRef]

152. Rybalova, E.; Strelkova, G.; Anishchenko, V. Mechanism of realizing a solitary state chimera in a ring of nonlocally coupled chaotic maps. *Chaos Solitons Fractals* **2018**, *115*, 300–305. [CrossRef]

153. Rybalova, E.; Schöll, E.; Strelkova, G. Controlling chimera and solitary states by additive noise in networks of chaotic maps. *J. Differ. Appl.* **2022**, 1–22. [CrossRef]

154. Chua, L.O.; Yang, L. Cellular neural networks: Theory. *IEEE Trans. Circuits Syst.* **1998**, *35*, 1257–1272. [CrossRef]

155. Chua, L.O.; Yang, L. Cellular neural networks: Applications. *IEEE Trans. Circuits Syst.* **1998**, *35*, 1273–1290. [CrossRef]

156. Chang, H.-M.; Juang, J. Piecewise two-dimensional maps and applications to cellular neural networks. *Int. J. Bifurc. Chaos* **2004**, *14*, 2223–2228. [CrossRef]

157. Chang, H.-M.; Juang, J. Boundary Influence on the Entropy of a Problem in Cellular Neural Networks. Master's Thesis, National Chiao Tung University, Taiwan, China, 2004. Available online: https://ir.nctu.edu.tw/bitstream/11536/52224/3/250303.pdf (accessed on 22 September 2023). (In English)

158. Skrynnyk, I.; Dmitrishin, D.; Stokolos, A.; Iacob, I.E. Computational aspects of large-length cycle search algorithms for nonlinear discrete systems. *Proc. Odessa Polytech. Univ.* **2019**, *58*, 69–84. Available online: http://dspace.opu.ua/jspui/handle/123456789/10522 (accessed on 28 July 2023). [CrossRef]

159. Shang, D.; Shang, P.; Liu, L. Multidimensional scaling method for complex time series feature classification based on generalized complexity-invariant distance. *Nonlinear Dyn.* **2019**, *95*, 2875–2892. [CrossRef]

160. Jacob, R.; Harikrishnan, K.P.; Misra, R.; Ambika, G. Measure for degree heterogeneity in complex networks and its application to recurrence network analysis. *R. Soc. Open Sci.* **2017**, *4*, 160757. [CrossRef]

161. Amigo, J.M.; Kennel, M.B. Topological permutation entropy. *Physica D* **2007**, *231*, 137–142. [CrossRef]

162. Mekler, A. Calculation of EEG correlation dimension: Large massifs of experimental data. *Comput. Methods Programs Biomed.* **2008**, *92*, 154–160. [CrossRef]

163. Yang, Y.; Duan, Z. An effective co-evolutionary algorithm based on artificial bee colony and differential evolution for time series predicting optimization. *Complex Intell. Syst.* **2020**, *6*, 299–308. [CrossRef]

164. Tang, T.W.; Allison, A.; Abbott, D. Investigation of chaotic switching strategies in Parrondo's games. *Fluct. Noise Lett.* **2004**, *4*, L585–L596. [CrossRef]

165. Harmer, G.P.; Abbott, D.; Taylor, P.G.; Parrondo, J.M.R. Brownian ratchets and Parrondo's games. *Chaos* **2001**, *11*, 705–714. [CrossRef] [PubMed]

166. Al-Hilli, W.H. Using Software's and Technology in Solving Mathematics Problem to Motivate and Accelerate the Learning Process. *EURASIA J. Math. Sci. Technol. Educ.* **2019**, *15*, em1670. [CrossRef] [PubMed]

167. Rodrigues, V. H. P.; Oliveira, T. R.; Cunha, J.P.V.S. Globally Stable Synchronization of Chaotic Systems Based on Norm Observers Connected in Cascade. *IEEE Trans. Circuits Syst. II Express Briefs* **2016**, *63*, 883–887. [CrossRef]

**Disclaimer/Publisher's Note:** The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.