Autonomous Jerk Oscillator with Quadratic Nonlinearities: Theoretical Investigations, Chaos Control, and Difference Synchronization

Adiyaman Y, Emiroglu S, Kursad Ucar M, Yildiz M (2020) Dynamical analysis, electronic circuit design and control application of a different chaotic system. Chaos Theory Appl 2:10–16 Agrawal SK, Srivastava M, Das S (2012) Synchronization of fractional order chaotic systems using active control method. Chaos Sol Fract 45:737–752 Ainamon C, Kingni ST, Kamdoum Tamba V, Chabi Orou JB, Woafo P (2019) Dynamics, circuitry implementation, and controlof an autonomous Helmholtz jerk oscillator. J Control Autom Electr Syst 30:501–511 Bensaid IFZ, González M, León-Saavedra F, de la Rosa MPR (2022) Hypercyclicity of operators that λ-commute with the differentiation operator on the space of entire functions. J Funct Anal 282:109391–109413 Cai N, Jing Y, Zhang S (2010) Modified projective synchronization of chaotic systems with disturbances via active sliding mode control. Commun Nonlinear SciNumer Simul 15:1613–1620 Chedjou JC, Fotsin HB, Woafo P, Domngang S (2001) Analog simulation of the dynamics of a van der Pol oscillator coupled to a Duffing oscillator. IEEE Trans Circuits Syst I(48):748–756 Chua L (1993) A universal circuit for studying and generating chaos-part II: stange attractors. IEEE Trans Circuits Syst I(40):182–186 Cuomo KM, Oppenheim AV, Strogatz SH (1993) Synchronization of Lorenz-based chaotic circuits with applications to communications. IEEE Trans Circuits Syst II Analog Dig Sig Process 40:626–633 Dana SK, Sengupta DC, Edoh KD (2001) Chaotic dynamics in Josephson junction. IEEE Trans Circuits Syst I(48):990–996 Das S, Yadav VK (2016) Chaos control and function projective synchronization of fractional-order systems through the backstepping method. Theor Math Phys 189:1430–1439 de la Rosa MPR (2009) Regular orbits and positive directions. Positivity 13:631–642 Dongmo ED, Ojo KS, Woafo P, Njah AN (2018) Difference synchronization of identical and nonidentical chaotic and hyperchaotic systems of different orders using active backstepping design. J Comput Nonlinear Dyn 13:051005 Fotsin HB, Woafo P (2005) Adaptive synchronization of a modified and uncertain chaotic van der Pol-Duffing oscillator based on parameter identification. Chaos, Solitons Fractals 24:1363–1371 Grassi G, Mascolo S (1999) Synchronizing high dimensional chaotic systems via eigenvalue placement with application to cellular neural networks. Int J Bifurc Chaos 9:705–711 Kemnang Tsafack AS, Kengne R, Cheukem A, Mboupda Pone JR, Kenne G (2020) Chaos control using self-feedback delay controller and electronic implementation in IFOC of 3-phase induction motor. Chaos Theory Appl 2:40–48 Kengne J, Chedjou JC, Kom M, Kyamakya K, Kamdoum Tamba V (2014) Regular oscillations, chaos, and multistability in a system of two coupled van der Pol oscillators: numerical and experimental studies. Nonlinear Dyn 76:1119–1132 Kengne J, Njitacke ZT, Nguomkam Negou A, Fouodji Tsostop M, Fotsin HB (2016) Coexistence of multiple attractors and crisis route to chaos in a novel chaotic jerk circuit. Int J Bifurc Chaos 26:1650081 Kengne J, Njitacke ZT, Fotsin HB (2016) Dynamical analysis of a simple autonomous jerk system with multiple attractors. Nonlinear Dyn 83:751–765 Kennedy MP, Rovatti R, Setti G, Raton B (eds) (2000) chaotic electronics in telecommunications. CRC, Boca Raton Kingni ST, Rajagopal K, Kamdoum Tamba V, Ainamon C, Chabi Orou JB (2019a) Analysis and FPGA implementation of an autonomous Josephson junction snap oscillator. Eur Phys J B 92:227 Kingni ST, Fautso Kuiate G, KamdoumTamba V, Pham V-T, Hoang DV (2019b) Self-excited and hidden attractors in autonomous Josephson jerk oscillator: analysis and its application to text encryption. J Comput Nonlinear Dyn 14:071004 Kvarda P (2002) chaos in Hartley’s oscillator. Int J Bifurc Chaos 12(10):2229–2232 León-Saavedra F, de la Rosa MPR (2022) A note on frequent hypercyclicity of operators that -commute with the differentiation operator. J Math Sci 266:615–620 Li C, Sprott JC (2016) Variable–boostable chaotic flows. Optik 127:10389–10398 Li GH, Zhou SP, Yang K (2006) Generalized projective synchronization between two different chaotic systems using active backstepping control. Phys Lett A 355:326–330 Li T, Yu J, Wang Z (2009) Delay-range-dependent synchronization criterion for Lur’e systems with delay feedback control. Commun Nonlinear Sci Numer Simul 14:1796–1803 Li C, Sprott JC, Yuan Z, Li H (2015) Constructing chaotic systems with total amplitude control. Int J Bifurc Chaos 25:1530025 Liao TL, Tsai SH (2000) Adaptive synchronization of chaotic systems and its application to secure communications. Chaos Sol Fract 11:1387–1396 Louodop P, Tchitnga R, Fagundes FF, Kountchou M, Kamdoun Tamba V, Carlos L, Pando L, Hilda A (2019) Cerdeira, extreme multistability in a Josephson-junction-based circuit. Phys Rev E 99:042208 Ma J (2022) Chaos theory and applications: the physical evidence, mechanism are important in chaotic systems. Chaos Theory Appl 4:1–3 Maggio GM, Di Bernardo M, Kennedy MP (2000a) Nonsmooth bifurcations in a piecewise linear model of the Colpitts oscillator. IEEE Trans Circuits Syst i Fundam Theory Appl 47:1160–1177 Maggio GM, De Feo O, Kennedy MP (2000b) Nonlinear analysis of the Colpitts oscillator and applications to design. IEEE Trans Circuits Syst I: Fundam Theory Appl 46:1118–1130 Nguimdo RM, Tchitnga R, Woafo P (2013) Dynamics of coupled simplest chaotic two-component electronic circuitsand its potential application to random bit generation. Chaos Interdiscip J Nonlinear Sci 23:43122 Ott E, Grebogi C, Yorke JA (1990) Controlling chaos. Phys Rev Lett 64:1196–1199 Pecora LM, Carroll TL (1990) Synchronization in chaotic systems. Phys Rev Lett 64:821 Rosenblum MG, Pikovsky AS, Kurths J (1996) Phase synchronization of chaotic oscillators. Phys Rev Lett 76:1804 Runzi L, Yinglan W, Shucheng D (2011) Combination synchronization of three classicchaotic systems using active backstepping design. Chaos 21:043114 Sprott JC (2000) Simple chaotic systems and circuits. Am J Phys 68:758–763 Sugiura T, Yamanashi Y, Yoshikawa N (2011) Demonstration of 30 Gbit/s generation of superconductive true random number generator. IEEE Trans Appl Supercond 21:843 Volos CK, Kyprianidis IM, Stouboulos IN (2012) A chaotic path planning generator for autonomous mobile robots. Robot Auton Syst 60:651–656 Volos CK, Kyprianidis IM, Stouboulos IN (2013) Image encryption process based on chaotic synchronization phenomena. Signal Process 93:1328–1340 Wu X, Lai D, Lu H (2012) Generalized synchronization of the fractional-order chaos in weighted complex dynamical networks with non-identical nodes. Nonlinear Dyn 69:667–683 Xia Y (2009) Lag synchronization of unknown chaotic delayed yang-yang-type fuzzyneural networks with noise perturbation based on adaptive control and parameter identification. IEEE Trans Neural Netw 20:1165 Xu Q, Zhang Q, Jiang T, Bao B, Chen M (2018) Chaos in a second-order non-autonomous Wien-bridge oscillator without extra nonlinearity. Circuit World 44:108–114 Yadav VK, Agrawal SK, Srivastava M, Das S (2017) Phase and anti-phase synchronizations of fractional order hyperchaotic systems with uncertainties and external disturbances using nonlinear active control method. Int J Dynam Control 5:259–268 Yadav VK, Shukla VK, Das S (2019) Difference synchronization among three chaotic systems with exponential term and its chaos control. Chaos Solitons Fractals 124:36–51 Yassen MT (2000) Chaos control of Chen chaotic dynamical system. Chaos, Solitons Fractals 15:271–283 Yassen MT (2006) Chaos control of chaotic dynamical systems using backstepping design. Chaos Solitons Fractals 27:537–548