A Novel Chaotic System With Boomerang-Shaped Equilibrium, Its Circuit Implementation and Application to Sound Encryption

Ahmed M, Shamsi U, Khan IR (2015) An enhanced image encryption algorithm using fractional chaotic system. Procedia Comput Sci 57:852–859 Akgul A, Hussain S, Pehlivan I (2016) A new three-dimensional chaotic system, its dynamical analysis and electronic circuit applications. Optik 127:7062–7071 Akgul A, Moroz I, Pehlivan I, Vaidyanathan S (2016) A new four-scroll chaotic attractor and its engineering applications. Optik 127:5491–5499 Azar AT, Vaidyanathan S (2016) Advances in Chaos theory and intelligent control. Springer, Berlin Bassham LE, Rukhin AL, Soto J, Nechvatal JR, Smid ME, Leigh SD, Levenson M, Vangel M, Heckert NA, Banks DL (2010) A statistical test suite for random and pseudorandom number generators for cryptographic applications. Technical report, National Institute of Standards and Technology Chen Y, Yang Q (2015) A new Lorenz-type hyperchaotic system with a curve of equilibria. Math Comput Simul 112:40–55 Danca MF, Kuznetsov F, Chen G (2017) Unusual dynamics and hidden attractors of the Rabinovich-Fabrikant system. Nonlinear Dyn 88(1):791–805 Dudkowski D, Prasad A, Kapitaniak T (2015) Perpetual points and hidden attractors in dynamical systems. Phys Lett A 379(40–41):2591–2596 Dudkowski D, Jafari S, Kapitaniak T, Kuznetsov NV, Leonov GA, Prasad A (2016) Hidden attractors in dynamical systems. Phys Rep 637:1–50 Gotthans T, Petrzela J (2015) New class of chaotic systems with circular equilibrium. Nonlinear Dyn 81(3):1143–1149 Gotthans T, Sprott JC, Petrzela J (2016) Simple chaotic flow with circle and square equilibrium. Int J Bifurc Chaos 26(8), Article ID 1650137 Guin A, Dandapathak M, Sarkar S, Sarkar BC (2017) Birth of oscillation in coupled non-oscillatory Rayleigh-Duffing oscillators. Commun Nonlinear Sci Numer Simul 42:420–436 Hu W, Ding D, Zhang Y, Wang N, Liang D (2017) Hopf bifurcation and chaos in a fractional order delayed memristor-based chaotic circuit system. Optik 130:189–200 Hu X, Liu C, Liu L, Ni J, Li S (2016) Multi-scroll hidden attractors in improved sprott a system. Nonlinear Dyn 86(3):1725–1734 Jafari S, Sprott JC (2013) Simple chaotic flows with a line equilibrium. Chaos, Solitons Fractals 57:79–84 Kacar S (2016) Analog circuit and microcontroller based RNG application of a new easy realizable 4D chaotic system. Optik 127:9551–9561 Kengne J, Tabekoueng ZN, Fotsin HB (2016) Coexistence of multiple attractors and crisis route to chaos in autonomous third order Duffing-Holmes type chaotic oscillators. Commun Nonlinear Sci Numer Simul 36:29–44 Kim D, Chang PH (2013) A new butterfly-shaped chaotic attractor. Results Phys 3:14–19 Kingni ST, Pham VT, Jafari S, Woafo P (2017) A chaotic system with an infinite number of equilibrium points located on a line and on a hyperbola and its fractional-order form. Chaos, Solitons Fractals 99(1):209–218 Kuznetsov N (2016) The Lyapunov dimension and its estimation via the Leonov method. Phys Lett A 380(25–26):2142–2149 Kuznetsov N, Leonov GA, Yuldashev MV, Yuldashev RV (2017) Hidden attractors in dynamical models of phase-locked loop circuits: limitations of simulation in MATLAB and SPICE. Commun Nonlinear Sci Numer Simul 51:39–49 Leonov G, Kuznetsov N, Mokaev T (2015) Hidden attractor and homoclinic orbit in Lorenz-like system describing convective fluid motion in rotating cavity. Commun Nonlinear Sci Numer Simul 28(1–3):166–174 Leonov GA, Kuznetsov NV, Vagaitsev VI (2011) Localization of hidden Chuas attractors. Phys Lett A 375(23):2230–2233 Leonov GA, Kuznetsov NV (2013) Hidden attractors in dynamical systems. From hidden oscillations in Hilbert-Kolmogorov, Aizerman and Kalman problems to hidden chaotic attractor in Chua circuits. Int J Bifurc Chaos 23(1), Article ID 1330002 Leonov GA, Kuznetsov NV, Kuznetsova OA, Seldedzhi AM, Vagaitsev VI (2011) Hidden oscillations in dynamical systems. Trans Syst Control 6:54–67 Li C, Sprott JC, Yuan Z, Li H (2015) Constructing chaotic systems with total amplitude control. Int J Bifurc Chaos 25(10), Article ID 1530025 Li C, Sprott JC, Thioc W (2014) Bistability in a hyperchaotic system with a line equilibrium. J Exp Theor Phys 118(3):494–500 Lin Y, Wang C (2016) Current-mode multi-scroll chaos generator employing CCCII. Electron Lett 52(15):1295–1297 Liu H, Ren B, Zhao Q, Li N (2016) Characterizing the optical chaos in a special type of small networks of semiconductor lasers using permutation entropy. Opt Commun 359:79–84 Liu W, Sun K, Zhu C (2016) A fast image encryption algorithm based on chaotic map. Opt Lasers Eng 84:26–36 Liu X, Mei W, Du H (2016) Simultaneous image compression, fusion and encryption algorithm based on compressive sensing and chaos. Opt Commun 366:22–32 Lorenz EN (1963) Deterministic nonperiodic flow. J Atmos Sci 20(2):130–141 Ma P (2014) Is there a name to this equation: \(\left( y - a | x |^b \right)^2 + (c x)^2 = d\)? https://math.stackexchange.com/questions/902120/is-there-a-name-to-this-equation-y-axb2-cx2-d. Accessed 1 Aug 2017 Misbah C (2017) Complex dynamics and morpohgenesis. Springer, Berlin Nayfeh AH, Balachandran B (2008) Applied nonlinear dynamics: analytical, computational and experimental methods. Wiley, New Jersey Pehlivan I, Moroz IM, Vaidyanathan S (2014) Analysis, synchronization and circuit design of a novel butterfly attractor. J Sound Vib 333(20):5077–5096 Pham VT, Vaidyanathan S, Volos CK, Jafari S (2015) Hidden attractors in a chaotic system with an exponential nonlinear term. Eur Phys J Spec Top 224(8):1507–1517 Pham VT, Jafari S, Volos C, Giakoumis A, Vaidyanathan S, Kapitaniak T (2016) A chaotic system with equilibria located on the rounded square loop and its circuit implementation. IEEE Trans Circuits Syst II Express Briefs 63(9):878–882 Pham VT, Jafari S, Wang X, Ma J (2016) A chaotic system with different shapes of equilibria. Int J Bifurc Chaos 26, Article ID 1650069 Pham VT, Volos C, Jafari S, Vaidyanathan S, Kapitaniak T, Wang X (2016) A chaotic system with different families of hidden attractors. Int J Bifurc Chaos 26(8), Article ID 1650139 Pham VT, Vaidyanathan S, Volos CK, Jafari S, Gotthans T (2017) A three-dimensional chaotic system with square equilibrium and noequilibrium. In: Azar AT, Vaidyanathan S (eds) Fractional order control and synchronization of chaotic systems. Springer, Berlin, pp 613–635 Rasappan S, Vaidyanathan S (2012) Global chaos synchronization of WINDMI and Coullet chaotic systems by backstepping control. Far East J Math Sci 67(2):265–287 Sambas A, Sanjaya WS, Mamat M (2015) Bidirectional coupling scheme of chaotic systems and its application in secure communication system. J Eng Sci Technol Rev 8(2):89–95 Sambas A, Vaidyanathan S, Mamat M, Sanjaya WM, Rahayu DS (2016) A 3-D novel jerk chaotic system and its application in secure communication system and mobile robot navigation. In: Vaidyanathan S, Volos C (eds) Advances and applications in Chaotic systems. Springer, Berlin, pp 283–310 Senouci A, Boukabou A (2016) Fuzzy modeling, stabilization and synchronization of multi-scroll chaotic systems. Optik 127(13):5351–5358 Sun J, Shen Y (2016) Compound-combination anti-synchronization of five simplest memristor chaotic systems. Optik 127(20):9192–9200 Tacha OI, Volos CK, Kyprianidis IM, Stouboulos IN, Vaidyanathan S, Pham VT (2016) Analysis, adaptive control and circuit simulation of a novel nonlinear finance system. Appl Math Comput 276:200–217 Vaidyanathan S (2015) Adaptive synchronization of chemical chaotic reactors. Int J Chem Tech Res 8(2):612–621 Vaidyanathan S (2016) A novel 3-D jerk chaotic system with three quadratic nonlinearities and its adaptive control. Arch Control Sci 26(1):19–47 Vaidyanathan S (2016) Anti-synchronization of 3-cells cellular neural network attractors via integral sliding mode control. Int J PharmTech Res 9(1):193–205 Vaidyanathan S (2016) Global chaos control of the FitzHugh-Nagumo chaotic neuron model via integral sliding mode control. Int J PharmTech Res 9(4):413–425 Vaidyanathan S, Azar AT (2016) Takagi-Sugeno fuzzy logic controller for Liu-Chen four-scroll chaotic system. Int J Intell Eng Inform 4:135–150 Vaidyanathan S, Rajagopal K (2017) LabVIEW implementation of chaotic masking with adaptively synchronised forced Van der Pol oscillators and its application in real-time image encryption. Int J Simul Process Model 12(2):165–178 Vaidyanathan S, Volos C (2015) Analysis and adaptive control of a novel 3-D conservative no-equilibrium chaotic system. Arch Control Sci 25(3):333–353 Vaidyanathan S, Volos C (2017) Advances in memristors, memristive devices and systems. Springer, Berlin Vaidyanathan S, Volos C, Thanh VT, Madhavan K, Idowu BA (2014) Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities. Arch Control Sci 24(3):257–285 Vaidyanathan S, Sambas A, Mamat M, Sanjaya WSM (2017) Analysis, synchronisation and circuit implementation of a novel jerk chaotic system and its application for voice encryption. Int J Model Ident Control 28(2):153–166 Volos C, Kyprianidis I, Stouboulos I, Tlelo-Cuautle E, Vaidyanathan S (2015) Memristor: a new concept in synchronization of coupled neuromorphic circuits. J Eng Sci Technol Rev 8(2):157–173 Volos CK, Kyprianidis IM, Stouboulos IN (2013) Image encryption process based on chaotic synchronization phenomena. Sig Process 93(5):1328–1340 Volos CK, Prousalis D, Kyprianidis I, Stouboulos I, Vaidyanathan S, Pham VT (2016) Synchronization and anti-synchronization of coupled Hindmarsh-Rose neuron models. Int J Control Theory Appl 9(1):101–114 Wang C, Zhang H, Fan W, Fan X (2016) A new wind power prediction method based on chaotic theory and Bernstein neural network. Energy 117:259–271 Wang X, Pham VT, Volos C (2017) Dynamics, circuit design and synchronization of a new chaotic system with closed curve equilibrium. Complexity 2017, Article ID 7138971 Wolf A, Swift JB, Swinney HL, Vastano J (1985) Determining Lyapunov exponents from a time series. Physica D 16(3):285–317 Wu T, Sun W, Zhang X, Zhang S (2016) Concealment of time delay signature of chaotic output in a slave semiconductor laser with chaos laser injection. Opt Commun 381:174–179 Xu C, Wu Y (2015) Bifurcation and control of chaos in a chemical system. Appl Math Model 39:2295–2310 Zhang C (2016) Theoretical design and circuit realization of complex grid multi-wing chaotic system. Optik 127:4584–4589 Zhang C, Yu S (2010) Generation of grid multi-scroll chaotic attractors via switching piecewise linear controller. Phys Lett A 374(30):3029–3037 Zhang J, Gao Y (2017) Synchronization of coupled neural networks with time-varying delay. Neurocomputing 219:154–162 Zhusubaliyev ZT, Mosekilde E (2015) Multistability and hidden attractors in a multilevel DC/DC converter. Math Comput Simul 109:32–45 Zhusubaliyev ZT, Mosekilde E, Rubanov VG, Nabokov R (2015) Multistability and hidden attractors in a relay system with hysteresis. Physica D 306:6–15