Emergence of complex dynamical behaviors in improved Colpitts oscillators: antimonotonicity, coexisting attractors, and metastable chaos

Emerging applications of chaotic oscillators require a classification and characterization of their complex behaviour with respect to their numerous parameters. In the present work, the dynamics of improved Colpitts oscillator is revisited based on a smooth (i.e. exponential) mathematical model of the system. In contrast to previous literature related to the improved Colpitts oscillator, the numerical simulations reveal very rich and striking phenomena including antimonotonicity, coexistence of attractors, and metastable chaos. Various complex dynamics regimes are characterized in terms of the system parameters by using bifurcation diagrams, Lyapunov exponents and phase space trajectory plots. Some PSpice simulations of the nonlinear dynamics of the oscillator are carried out to validate the theoretical analysis. Owing to the richness of bifurcation modes observed in this work, the improved Colpitts oscillator may be useful in theoretical, numerical and experimental studies of various aspects of nonlinear dynamics in autonomous systems and related topics. It also has promising applications in the fields of High Frequency chaos based communications, sonar sensors as well as radar systems.

[1]  Krishnamurthy Murali,et al.  The smallest transistor-based nonautonomous chaotic circuit , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[2]  Julien Clinton Sprott,et al.  Coexisting Hidden Attractors in a 4-D Simplified Lorenz System , 2014, Int. J. Bifurc. Chaos.

[3]  Masoller.  Coexistence of attractors in a laser diode with optical feedback from a large external cavity. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[4]  J. Yorke,et al.  Antimonotonicity: inevitable reversals of period-doubling cascades , 1992 .

[5]  A. Tamasevicius,et al.  Improved chaotic Colpitts oscillator for ultrahigh frequencies , 2004 .

[6]  Shandelle M Henson,et al.  Multiple mixed-type attractors in a competition model , 2007, Journal of biological dynamics.

[7]  Ingo Fischer,et al.  Synchronization of chaotic semiconductor laser dynamics on subnanosecond time scales and its potential for chaos communication , 2000 .

[8]  Xiao-Song Yang,et al.  Chaos and transient chaos in simple Hopfield neural networks , 2005, Neurocomputing.

[9]  Ulrich Parlitz,et al.  Superstructure in the bifurcation set of the Duffing equation ẍ + dẋ + x + x3 = f cos(ωt) , 1985 .

[10]  P. Woafo,et al.  Dynamics of coupled simplest chaotic two-component electronic circuits and its potential application to random bit generation. , 2013, Chaos.

[11]  Ioannis M. Kyprianidis,et al.  Antimonotonicity and Chaotic Dynamics in a Fourth-Order Autonomous nonlinear Electric Circuit , 2000, Int. J. Bifurc. Chaos.

[12]  Christophe Letellier,et al.  Symmetry groups for 3D dynamical systems , 2007 .

[13]  Ogawa.  Quasiperiodic instability and chaos in the bad-cavity laser with modulated inversion: Numerical analysis of a Toda oscillator system. , 1988, Physical review. A, General physics.

[14]  A. Nayfeh,et al.  Applied nonlinear dynamics : analytical, computational, and experimental methods , 1995 .

[15]  J. Yorke,et al.  Crises, sudden changes in chaotic attractors, and transient chaos , 1983 .

[16]  Antanas Cenys,et al.  Two-stage chaotic Colpitts oscillator , 2001 .

[17]  A. Uchida,et al.  Dual synchronization of chaos in Colpitts electronic oscillators and its applications for communications. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Luigi Fortuna,et al.  Chaotic pulse position modulation to improve the efficiency of sonar sensors , 2003, IEEE Trans. Instrum. Meas..

[19]  Marcelo A. Savi,et al.  Chaos and transient chaos in an experimental nonlinear pendulum , 2006 .

[20]  Kyandoghere Kyamakya,et al.  Dynamical properties and chaos synchronization of improved Colpitts oscillators , 2012 .

[21]  Ioannis M. Kyprianidis,et al.  Image encryption process based on chaotic synchronization phenomena , 2013, Signal Process..

[22]  Sara Dadras,et al.  Analysis of a new 3D smooth autonomous system with different wing chaotic attractors and transient chaos , 2010 .

[23]  B. R. Nana Nbendjo,et al.  Hyperchaos and bifurcations in a driven Van der Pol–Duffing oscillator circuit , 2015 .

[24]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[25]  L. Larger,et al.  Nonlocal Nonlinear Electro-Optic Phase Dynamics Demonstrating 10 Gb/s Chaos Communications , 2010, IEEE Journal of Quantum Electronics.

[26]  Parlitz,et al.  Period-doubling cascades and devil's staircases of the driven van der Pol oscillator. , 1987, Physical review. A, General physics.

[27]  James A. Yorke,et al.  Metastable chaos: The transition to sustained chaotic behavior in the Lorenz model , 1979 .

[28]  Laurent Larger,et al.  Electro-optical chaos for multi-10 Gbit/s optical transmissions , 2004 .

[29]  Tassos Bountis,et al.  Remerging Feigenbaum trees in dynamical systems , 1984 .

[30]  Michael Peter Kennedy,et al.  Nonlinear analysis of the Colpitts oscillator and applications to design , 1999 .

[31]  D. Gauthier,et al.  High-speed chaos in an optical feedback system with flexible timescales , 2003, IEEE Journal of Quantum Electronics.

[32]  Steven H. Strogatz,et al.  Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering , 1994 .

[33]  Mohammed-Salah Abdelouahab,et al.  Hopf bifurcation and chaos in fractional-order modified hybrid optical system , 2012 .

[34]  Vaithianathan Venkatasubramanian,et al.  Coexistence of four different attractors in a fundamental power system model , 1999 .

[35]  Antonio Politi,et al.  COLLISION OF FEIGENBAUM CASCADES , 1984 .

[36]  Ludovico Minati,et al.  Experimental dynamical characterization of five autonomous chaotic oscillators with tunable series resistance. , 2014, Chaos.

[37]  P. Philominathan,et al.  Composite dynamical behaviors in a simple series–parallel LC circuit , 2012 .

[38]  Grebogi,et al.  Geometric mechanism for antimonotonicity in scalar maps with two critical points. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[39]  Leon O. Chua,et al.  EXPERIMENTAL OBSERVATION OF ANTIMONOTONICITY IN CHUA'S CIRCUIT , 1993 .

[40]  F. M. Izrailev,et al.  Transient chaos in a generalized Hénon map on the torus , 1988 .

[41]  D. C. Hamill.  Learning about chaotic circuits with SPICE , 1993 .

[42]  B. Z. Essimbi,et al.  Synchronization of improved chaotic Colpitts oscillators using nonlinear feedback control , 2009 .

[43]  Jing Xia Li,et al.  Experimental demonstration of 1.5 GHz chaos generation using an improved Colpitts oscillator , 2013 .