Generalized Adaptive Backstepping Synchronization for Non-Identical Parametrically Excited Systems

In this paper, we investigate the synchronization of chaotic systems consisting of non-identical parametrically excited oscillators. The backstepping design, which is a recursive procedure that combines the choice of a Lyapunov function with the design of a controller is generalized and employed so as to achieve global chaos synchronization between a parametrically excited gyroscope and each of the parametrically excited pendulum and Duffing oscillator. Numerical simulations are implemented to verify the results

Bifurcation and Chaos in Coupled Ratchets exhibiting Synchronized Dynamics

The bifurcation and chaotic behaviour of unidirectionally coupled deterministic ratchets is studied as a function of the driving force amplitude ($a$) and frequency ($\omega$). A classification of the various types of bifurcations likely to be encountered in this system was done by examining the stability of the steady state in linear response as well as constructing a two-parameter phase diagram in the ($a -\omega$) plane. Numerical explorations revealed varieties of bifurcation sequences including quasiperiodic route to chaos. Besides, the familiar period-doubling and crises route to chaos exhibited by the one-dimensional ratchet were also found. In addition, the coupled ratchets display symmetry-breaking, saddle-nodes and bubbles of bifurcations. Chaotic behaviour is characterized by using the sensitivity to initial condition as well as the Lyapunov exponent spectrum; while a perusal of the phase space projected in the Poincar$\acute{e}$ cross-section confirms some of the striking features.Comment: 7 pages; 8 figure

Hyperchaos and bifurcations in a driven Van der Pol–Duffing oscillator circuit

We investigate the dynamics of a driven Van der Pol–Duffing oscillator circuit and show the existence of higher-dimensional chaotic orbits (or hyperchaos), transient chaos, strange-nonchaotic attractors, as well as quasiperiodic orbits born from Hopf bifurcating orbits. By computing all the Lyapunov exponent spectra, scanning a wide range of the driving frequency and driving amplitude parameter space, we explore in two-parameter space the regimes of different dynamical behaviours

Phase synchronization of coupled hyper-chaotic duffing oscillator

No AbstractJournal of the Nigerian Association of Mathematical Physics Vol. 8 2004: pp. 203-21

Control and Synchronization of Chaotic and Hyperchaotic Lorenz Systems via Extended Backstepping Techniques

We propose novel controllers for stabilization and tracking of chaotic and hyperchaotic Lorenz systems using extended backstepping techniques. Based on the proposed approach, generalized weighted controllers were designed to control chaotic behaviour as well as to achieve synchronization in chaotic and hyperchaotic Lorenz systems. The effectiveness and feasibility of the proposed weighted controllers were verified numerically and showed their robustness against noise

Comparative study of chaotic features in hourly wind speed using recurrence quantification analysis

Due to the shortage in electricity supply in Nigeria, there is a need to improve the alternative power generation from wind energy by analysing the wind speed data available in some parts of the country, for a better understanding of its underlying dynamics for the purpose of good prediction and modelling. The wind speed data used in this study were collected over a period of two years by National Space Research and Development Agency (NASRDA) from five different stations in the tropics namely; Abuja (7050'02.09"N and 6004'29.97"E), Akungba (6059'05.40"N and 5035'52.23"E), Nsukka (6051'28.14"N and 7024'28.15"E), Port Harcourt (4047'05.41"N and 6059'30.62"E), and Yola (9017'33.58"N and 12023'26.69"E). In this paper, recurrence plot (RP) and recurrence quantification analysis (RQA) are applied to investigate a non-linear deterministic dynamical process and non-stationarity in hourly wind speed data from the study areas. Using RQA for each month of the two years, it is observed that wind speed data for the wet months exhibit higher chaoticity than that of the dry months for all the stations, due to strong and weak monsoonal effect during the wet and dry seasons respectively. The results show that recurrence techniques are able to identify areas and periods for which the harvest of wind energy for power generation is good (high predictability) and poor (low predictability) in the study areas. This work also validates the RQA measures (Lmax, DET and ENT) used and establishes that they are similar/related as they give similar results for the dynamical characterization of the wind speed data

Compound-combination synchronization of chaos in identical and different orders chaotic systems

This paper proposes a new synchronization scheme called compound-combination synchronization. The scheme is investigated using six chaotic Josephson junctions evolving from different initial conditions based on the drive-response configuration via the active backstepping technique. The technique is applied to achieve compound-combination synchronization of: (i) six identical third order resistive-capacitive-inductive-shunted Josepshon junctions (RCLSJJs) (with three as drive and three as response systems); (ii) three third order RCLSJJs (as drive systems) and three second order resistive-capacitive-shunted Josepshon junctions (RCSJJs (as response systems). In each case, sufficient conditions for global asymptotic stability for compound-combination synchronization to any desired scaling factors are achieved. Numerical simulations are employed to verify the feasibility and effectiveness of the compound-combination synchronization scheme. The result shows that this scheme could be used to vary the junction signal to any desired level and also give a better insight into synchronization in biological systems wherein different organs of different dynamical structures and orders are involved. The scheme could also provide high security in information transmission due to the complexity of its dynamical formulation