Volume 7 (2017)  

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1.  Dynamical behavior of Peter-De-Jong map using the modi ed 0-1 and 3ST tests for chaos  Full text (PDF)

Thierry Tanze Wontchuim, Joseph Yves E a, Henri Paul Ekobena Fouda, Jean Sire Armand Eyebe Fouda

Pages: 1-21

Abstract:  In this paper, a detailed analysis of the behavior of Peter-De-Jong map using the modi ed 0-1 and 3ST tests is presented. The results show that both tests work well and e ectively distinguish chaotic and regular motions in all the studied cases. The simulation times necessary in all the cases are largely inferior to the ones obtained using the 0-1 test which requires long data sets to perform well. We also performed some comparisons between the 0-1 test and the 3ST test for the litigious cases for which the decision by the 0-1 method is ambiguous, and we claim that the 3ST test can be a good alternative to the 0-1 method. The 3ST test is a very e cient method and is particularly useful in characterizing the quasi-periodic motion.

2. Limits of Solutions of a Recurrence Relation with Bang Bang Control Full text (PDF)    

Jiannan Songm, Fan Wu, Chengmin Hou

Pages: 22-40

Abstract:  In this paper, we consider a three term nonlinear recurrence. We are able to derive the exact relations between the initial values and with the limiting behaviors of the solution determined by them.

3. Effect of Narrow Band Frequency Modulated Signal on Horseshoe Chaos in Nonlinearly Damped Duffing-vander Pol Oscillator   Full text (PDF)

M.V. Sethumeenakshim, S. Athisayanathan, V. Chinnathambi, S. Rajasekar                                                                                                       

Pages: 41-55

Abstract:  This paper invsetigates both analytically and numerically the effect of narrow band frequency modulated (NBFM) signal on horseshoe chaos in nonlinearly damped Duffing-vander Pol oscillator (DVP) system. Using the Melnikov analytical method, we obtain the threshold condition for the onset of horseshoe chaos. Threshold curves are drawn in various parameters spaces. We identify the regions of horseshoe chaos in various parameters spaces and bring out the e ect of NBFM signal in DVP system. We illustrate that by varying the parameters f, g, p, one can suppress or enhance horseshoe chaos. We confirm the analytical results by the numerical tools such as computation of stable and unstable manifolds of saddle and threshold curves.

4.  Coexistence of multiple attractors, Hysteresis and Vibrational resonance in Chua's circuit driven by an Amplitude modulated force

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V. Bala Shunmuga Jothi, S. Selvaraj, V. Chinnathambi, V. Chinnathambi, S. Rajasekar                                                                                                     

Pages: 56-67

Abstract:  We consider a single scroll Chua's circuit driven by an amplitude modulated force (AMF) with two widely different frequencies. Numerically we study the dynamics of Chua's circuit driven by an AMF for specific set of values of the parameters. We show the occurrence of coexistence of several period-T orbits, bifurcations of them, period-doubling route to chaos, quasiperiodic orbit, hysteresis and vibrational resonance phenomena. We characterize periodic, quasiperiodic and chaotic orbits, hysteresis and vibrational resonance phenomena using bifurcation diagram, phase portrait, Poincar2 surface of section, trajectory and resonance plots.

5.  Compound synchronization of different chaotic systems based on active backstepping control

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R. Sivasamy                                                                                               

Pages: 57-80

Abstract:  In this paper, compound synchronization of four different chaotic systems based on active backstepping control is investigated. For the synchronization purpose three master systems and one slave system are considered. According to Lyapunov stability theory, we design suitable active controller which is able to achieve compound synchronization between master and slave systems. Finally numerical simulations are provided to show the e effectiveness of the proposed controller. In the numerical simulations, chaotic Lorenz, Rossler and Chen systems are considered as master systems and Lu system is considered as a slave system.