Displaying all 13 publications

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  1. Muthukumar P, Balasubramaniam P, Ratnavelu K
    Chaos, 2014 Sep;24(3):033105.
    PMID: 25273185 DOI: 10.1063/1.4886355
    In this paper, we design a new three dimensional King Cobra face shaped fractional order chaotic system. The multi-scale synchronization scheme of two fractional order chaotic systems is described. The necessary conditions for the multi-scale synchronization of two identical fractional order King Cobra chaotic systems are derived through feedback control. A new cryptosystem is proposed for an image encryption and decryption by using synchronized fractional order King Cobra chaotic systems with the supports of multiple cryptographic assumptions. The security of the proposed cryptosystem is analyzed by the well known algebraic attacks. Numerical simulations are given to show the effectiveness of the proposed theoretical results.
  2. Alias A, Grimshaw RH, Khusnutdinova KR
    Chaos, 2013 Jun;23(2):023121.
    PMID: 23822486 DOI: 10.1063/1.4808249
    In the weakly nonlinear limit, oceanic internal solitary waves for a single linear long wave mode are described by the KdV equation, extended to the Ostrovsky equation in the presence of background rotation. In this paper we consider the scenario when two different linear long wave modes have nearly coincident phase speeds and show that the appropriate model is a system of two coupled Ostrovsky equations. These are systematically derived for a density-stratified ocean. Some preliminary numerical simulations are reported which show that, in the generic case, initial solitary-like waves are destroyed and replaced by two coupled nonlinear wave packets, being the counterpart of the same phenomenon in the single Ostrovsky equation.
  3. Banerjee S, Theesar SJ, Kurths J
    Chaos, 2013 Mar;23(1):013118.
    PMID: 23556955 DOI: 10.1063/1.4791589
    We study generalized variable projective synchronization between two unified time delayed systems with constant and modulated time delays. A novel Krasovskii-Lyapunov functional is constructed and a generalized sufficient condition for synchronization is derived analytically using the Lyapunov stability theory and adaptive techniques. The proposed scheme is valid for a system of n-numbers of first order delay differential equations. Finally, a new neural oscillator is considered as a numerical example to show the effectiveness of the proposed scheme.
  4. Lan BL
    Chaos, 2006 Sep;16(3):033107.
    PMID: 17014212
    The dynamics of a periodically delta-kicked Hamiltonian system moving at low speed (i.e., at speed much less than the speed of light) is studied numerically. In particular, the trajectory of the system predicted by Newtonian mechanics is compared with the trajectory predicted by special relativistic mechanics for the same parameters and initial conditions. We find that the Newtonian trajectory, although close to the relativistic trajectory for some time, eventually disagrees completely with the relativistic trajectory, regardless of the nature (chaotic, nonchaotic) of each trajectory. However, the agreement breaks down very fast if either the Newtonian or relativistic trajectory is chaotic, but very much slower if both the Newtonian and relativistic trajectories are nonchaotic. In the former chaotic case, the difference between the Newtonian and relativistic values for both position and momentum grows, on average, exponentially. In the latter nonchaotic case, the difference grows much slower, for example, linearly on average.
  5. Banerjee S, Palit SK, Mukherjee S, Ariffin M, Rondoni L
    Chaos, 2016 Mar;26(3):033105.
    PMID: 27036183 DOI: 10.1063/1.4941374
    Reconstruction of phase space is an effective method to quantify the dynamics of a signal or a time series. Various phase space reconstruction techniques have been investigated. However, there are some issues on the optimal reconstructions and the best possible choice of the reconstruction parameters. This research introduces the idea of gradient cross recurrence (GCR) and mean gradient cross recurrence density which shows that reconstructions in time frequency domain preserve more information about the dynamics than the optimal reconstructions in time domain. This analysis is further extended to ECG signals of normal and congestive heart failure patients. By using another newly introduced measure-gradient cross recurrence period density entropy, two classes of aforesaid ECG signals can be classified with a proper threshold. This analysis can be applied to quantifying and distinguishing biomedical and other nonlinear signals.
  6. Batten JA, Lucey BM, Peat M
    Chaos, 2018 Dec;28(12):123109.
    PMID: 30599539 DOI: 10.1063/1.5029226
    The compass rose pattern in financial data may indicate the presence of a nonlinear, possibly chaotic, data generating mechanism. The analysis of three key financial asset and denoised returns, gold, the Great British Pound/US dollar spot exchange rate, and the Standard & Poor's 500 stock index, reveals that over four equivalent subperiods, from 1996 to 2015, the compass rose pattern changes. This finding provides an opportunity to establish how noise affects financial time series. We conclude that the compass rose pattern is unlikely the product of an underlying nonlinear structure, since there is evidence of nonlinearity in all time periods, even those where the compass rose pattern is not evident. Therefore, the compass rose patterns, seen in the denoised data, suggest that the presence of noise masks the underlying dynamics of the asset returns.
  7. Salahshour S, Ahmadian A, Salimi M, Ferrara M, Baleanu D
    Chaos, 2019 Aug;29(8):083110.
    PMID: 31472490 DOI: 10.1063/1.5096022
    Realizing the behavior of the solution in the asymptotic situations is essential for repetitive applications in the control theory and modeling of the real-world systems. This study discusses a robust and definitive attitude to find the interval approximate asymptotic solutions of fractional differential equations (FDEs) with the Atangana-Baleanu (A-B) derivative. In fact, such critical tasks require to observe precisely the behavior of the noninterval case at first. In this regard, we initially shed light on the noninterval cases and analyze the behavior of the approximate asymptotic solutions, and then, we introduce the A-B derivative for FDEs under interval arithmetic and develop a new and reliable approximation approach for fractional interval differential equations with the interval A-B derivative to get the interval approximate asymptotic solutions. We exploit Laplace transforms to get the asymptotic approximate solution based on the interval asymptotic A-B fractional derivatives under interval arithmetic. The techniques developed here provide essential tools for finding interval approximation asymptotic solutions under interval fractional derivatives with nonsingular Mittag-Leffler kernels. Two cases arising in the real-world systems are modeled under interval notion and given to interpret the behavior of the interval approximate asymptotic solutions under different conditions as well as to validate this new approach. This study highlights the importance of the asymptotic solutions for FDEs regardless of interval or noninterval parameters.
  8. Lan BL, Liew YW, Toda M, Kamsani SH
    Chaos, 2020 May;30(5):053137.
    PMID: 32491883 DOI: 10.1063/1.5130524
    Complex dynamical systems can shift abruptly from a stable state to an alternative stable state at a tipping point. Before the critical transition, the system either slows down in its recovery rate or flickers between the basins of attraction of the alternative stable states. Whether the heart critically slows down or flickers before it transitions into and out of paroxysmal atrial fibrillation (PAF) is still an open question. To address this issue, we propose a novel definition of cardiac states based on beat-to-beat (RR) interval fluctuations derived from electrocardiogram data. Our results show the cardiac state flickers before PAF onset and termination. Prior to onset, flickering is due to a "tug-of-war" between the sinus node (the natural pacemaker) and atrial ectopic focus/foci (abnormal pacemakers), or the pacing by the latter interspersed among the pacing by the former. It may also be due to an abnormal autonomic modulation of the sinus node. This abnormal modulation may be the sole cause of flickering prior to termination since atrial ectopic beats are absent. Flickering of the cardiac state could potentially be used as part of an early warning or screening system for PAF and guide the development of new methods to prevent or terminate PAF. The method we have developed to define system states and use them to detect flickering can be adapted to study critical transition in other complex systems.
  9. Natiq H, Banerjee S, Ariffin MRK, Said MRM
    Chaos, 2019 Jan;29(1):011103.
    PMID: 30709147 DOI: 10.1063/1.5079886
    In this paper, we investigate the dynamical behavior in an M-dimensional nonlinear hyperchaotic model (M-NHM), where the occurrence of multistability can be observed. Four types of coexisting attractors including single limit cycle, cluster of limit cycles, single hyperchaotic attractor, and cluster of hyperchaotic attractors can be found, which are unusual behaviors in discrete chaotic systems. Furthermore, the coexistence of asymmetric and symmetric properties can be distinguished for a given set of parameters. In the endeavor of chaotification, this work introduces a simple controller on the M-NHM, which can add one more loop in each iteration, to overcome the chaos degradation in the multistability regions.
  10. Miron P, Beron-Vera FJ, Olascoaga MJ, Koltai P
    Chaos, 2019 Apr;29(4):041105.
    PMID: 31042951 DOI: 10.1063/1.5092132
    Markov-chain models are constructed for the probabilistic description of the drift of marine debris from Malaysian Airlines flight MH370. En route from Kuala Lumpur to Beijing, MH370 mysteriously disappeared in the southeastern Indian Ocean on 8 March 2014, somewhere along the arc of the 7th ping ring around the Inmarsat-3F1 satellite position when the airplane lost contact. The models are obtained by discretizing the motion of undrogued satellite-tracked surface drifting buoys from the global historical data bank. A spectral analysis, Bayesian estimation, and the computation of most probable paths between the Inmarsat arc and confirmed airplane debris beaching sites are shown to constrain the crash site, near 25°S on the Inmarsat arc.
  11. Mahmud MN, Siri Z, Vélez JA, Pérez LM, Laroze D
    Chaos, 2020 Jul;30(7):073109.
    PMID: 32752617 DOI: 10.1063/5.0002846
    The control effects on the convection dynamics in a viscoelastic fluid-saturated porous medium heated from below and cooled from above are studied. A truncated Galerkin expansion was applied to balance equations to obtain a four-dimensional generalized Lorenz system. The dynamical behavior is mainly characterized by the Lyapunov exponents, bifurcation, and isospike diagrams. The results show that within a range of moderate and high Rayleigh numbers, proportional controller gain is found to enhance the stabilization and destabilization effects on the thermal convection. Furthermore, due to the effect of viscoelasticity, the system exhibits remarkable topological structures of regular regions embedded in chaotic domains.
  12. Abutalib M, Batle J, Ooi CH
    Chaos, 2016 Jul;26(7):073113.
    PMID: 27475073 DOI: 10.1063/1.4959138
    The total electrostatic energy of systems of identical particles of equal charge is studied in configurations bounded in space, but divergent in the number of charges. This approach shall guide us to unveil a non-linear, functional form specifying the divergent nature of system energy. We consider fractals to be physical entities, with charges located in their vertices or nodes. This description is interesting since features, such as the corresponding fractal dimension, can characterize the total energy EN. Finally, at local length scales, we describe how energy diverges at charge accumulation points in the fractal, that is, almost everywhere by definition.
  13. Vignesh D, Banerjee S
    Chaos, 2023 Mar;33(3):033126.
    PMID: 37003836 DOI: 10.1063/5.0139967
    Chemical reactions form the basis of life and understanding the different patterns and unpredictable changes in the reactions are noteworthy in real life situations. The article aims at constructing a mathematical model of two step reversible chemical reactions with a Caputo fractional difference operator. The reversible reaction involves the breakdown of an ester compound in the presence of water followed by the formation of fatty acid salts from the reaction of a free fatty acid with alkali hydroxide, such as NaOH. Using bifurcation diagrams, the chaotic response exhibited by the system is illustrated for state variables with identical fractional order and variables with non-identical fractional orders. The changes in periodic states of the system are investigated for each state variables with time varying plots and maximum Lyapunov exponents using the Jacobian matrix method are presented in support of the bifurcation diagrams. The synchronization of the subsystems of the proposed system is achieved with nonlinear control functions. Numerical simulations are presented to provide comparison of commensurate and incommensurate order models. Understanding the nature of these processes has significant applications in the production of bio-fuels from vegetable oils and animal fats by a transesterification reaction.
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