Qualification: 
Ph.D, MSc, BSc
b_rakshit@cb.amrita.edu

Dr. Biswambhar Rakshit currently serves as Assistant Professor at the Department of Mathematics, Amrita School of Engineering, Coimbatore Campus.

Dr. Biswambhar Rakshit received his Ph.D in Mathematics from the Indian Institute of Technology Kharagpur (IIT Kgp) under the supervision of Prof. Soumitro Banerjee. Before joining Amrita University Dr. Rakshit has worked as a postdoctoral fellow at the University of Tokyo, Japan, and as a Lecturer at National institute of Technology, Hamirpur, India.

His research interests include Complex Systems, Nonlinear Dynamics and Stochastic Systems. Currently he is working on Emergent Behaviour in Network of Coupled Oscillators having its applicability in modeling various self-organized complex ecological and biological systems.

Publications

Publication Type: Journal Article

Year of Publication Title

2020

Amit Sharma and Dr. Biswambhar Rakshit, “Enhancement of dynamical robustness in a mean-field coupled network through self-feedback delay”, arXiv preprint arXiv:2007.13405, 2020.[Abstract]


In this article, we propose a very efficient technique to enhance the dynamical robustness for a network of mean-field coupled oscillators experiencing aging transition. In particular, we present a control mechanism based on delayed negative self-feedback, which can effectively enhance dynamical activities in a mean-field coupled network of active and inactive oscillators. Even for a small value of delay, robustness gets enhanced to a significant level. In our proposed scheme, the enhancing effect is more pronounced for strong coupling. To our surprise even if all the oscillators perturbed to equilibrium mode delayed negative self-feedback able to restore oscillatory activities in the network for strong coupling strength. We demonstrate that our proposed mechanism is independent of coupling topology. For a globally coupled network, we provide numerical and analytical treatment to verify our claim. Also, for global coupling to establish the generality of our scheme, we validate our results for both Stuart-Landau limit cycle oscillators and chaotic Rossler oscillators. To show that our scheme is independent of network topology, we also provide numerical results for the local mean-field coupled complex network.

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2020

Dr. Biswambhar Rakshit, Niveditha Rajendrakumar, and B. Balaram, “Dangerous Aging Transition in a Network of Coupled Oscillators”, arXiv preprint arXiv:2007.13380, 2020.[Abstract]


In this article, we investigate the dynamical robustness in a network of relaxation oscillators. In particular, we consider a network of diffusively coupled Van der Pol oscillators to explore the aging transition phenomena. Our investigation reveals that the mechanism of aging transition in a network of Van der Pol oscillator is quite different from that of typical sinusoidal oscillators such as Stuart-Landau oscillators. Unlike sinusoidal oscillators, the order parameter does not follow the second-order phase transition. Rather we observe an abnormal phase transition of the order parameter due to sudden unbounded trajectories at a critical point. We call it a dangerous aging transition. We provide details bifurcation analysis of such abnormal phase transition. We show that the boundary crisis of a limit-cycle oscillator is at the helm of such a dangerous aging transition.

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2020

Dr. Biswambhar Rakshit, Niveditha Rajendrakumar, and B. Balaram, “Abnormal route to aging transition in a network of coupled oscillators”, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 30, no. 10, 2020.[Abstract]


In this article, we investigate the dynamical robustness in a network of Van der Pol oscillators. In particular, we consider a network of diffusively coupled Van der Pol oscillators to explore the aging transition phenomena. Our investigation reveals that the route to aging transition in a network of Van der Pol oscillator is different from that of typical sinusoidal oscillators such as Stuart–Landau oscillators. Unlike sinusoidal oscillators, the order parameter does not follow smooth second-order phase transition. Rather, we observe an abnormal phase transition of the order parameter due to the sudden appearance of unbounded trajectories at a critical point. We provide detailed bifurcation analysis of such an abnormal phase transition. We show that the boundary crisis of a limit-cycle oscillator is at the helm of such an unusual discontinuous path of aging transition.
The network of coupled oscillators is an efficient model to explore various self-organizing activities of complex systems in the disciplines of physics, biology, and engineering. Having robust oscillatory dynamics is a prerequisite for the normal functioning of such complex systems. The rhythmic activities of such a large-scale system should be resilient against any local degradation or deterioration. In the absence of any rhythmic activities, the regular functioning of many natural and man-made systems may face severe disruption and this emergent phenomenon is known as aging transition. Recently, the study of the robustness of the oscillatory dynamics of a complex dynamical system has become an emerging area of research. The basic framework of such an investigation involves a network of oscillatory nodes where some components of nodes are functionally degraded but not removed. Until now, the investigation of dynamical robustness was mainly limited to coupled Stuart–Landau oscillators, which have typical sinusoidal oscillation. However, there are many natural systems that can be modeled by a network non-sinusoidal oscillators such as Van der Pol oscillator. Van der Pol oscillator has been used to model many real-life systems that includes neuronal activities in the brain cortex and cardiac rhythms. In this article, we have studied the aging transition in a network of Van der Pol oscillators. Our investigation reveals some interesting phenomena. The order parameter that represents the dynamical activities in the network goes through an abnormal phase transition and suddenly blows up to infinity. We provide detailed bifurcation analysis for such an abnormal phase transition. A blue-sky catastrophe of a limit-cycle oscillator is responsible for the unbounded dynamics of the oscillators. Our results provide significant insights into the aging transition of complex dynamical systems where individual nodes represent a Van der Pol oscillator.

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2018

Srilena Kundu, Soumen Majhi, Partha Karmakar, Dibakar Ghosh, and Dr. Biswambhar Rakshit, “Augmentation of dynamical persistence in networks through asymmetric interaction”, EPL (Europhysics Letters), vol. 123, p. 30001, 2018.[Abstract]


There exists several natural instances in which systems may undergo through local degradation of its constituting elements. This may severely affect the overall dynamical activity in unexpected ways. So, it requires to overcome such situations while posing some appropriate mechanisms. In this work we investigate aging networks comprising different groups of dynamical units coupled locally, non-locally or globally. We provide a mechanism that deals with asymmetry in the interaction of active and inactive groups to enhance the dynamical robustness of such aging networks. Apart from numerical experiments, we provide analytical treatment to identify the critical phase transition. Mathematical results are found to perfectly match the outcomes obtained through numerical experiments. Moreover, we provide evidence of the enriched network survivability in more complex topologies considering small-world and scale-free networks. Our proposed method to enhance the dynamical robustness is thus independent of coupling topology and quite efficient in aging networks of coupled oscillators. More »»

2017

Srilena Kundu, Soumen Majhi, Sourav Kumar Sasmal, Dibakar Ghosh, and Dr. Biswambhar Rakshit, “Survivability of a metapopulation under local extinctions”, Physical Review E, vol. 96, 2017.[Abstract]


A metapopulation structure in landscape ecology comprises a group of interacting spatially separated subpopulations or patches of the same species that may experience several local extinctions. This makes the investigation of survivability (in the form of global oscillation) of a metapopulation on top of diverse dispersal topologies extremely crucial. However, among various dispersal topologies in ecological networks, which one can provide higher metapopulation survivability under local extinction is still not well explored. In this article, we scrutinize the robustness of an ecological network consisting of prey-predator patches having Holling type I functional response, against progressively extinct population patches. We present a comprehensive study on this while considering global, small-world, and scale-free dispersal of the subpopulations. Furthermore, we extend our work in enhancing survivability in the form of sustained global oscillation by introducing asymmetries in the dispersal rates of the considered species. Our findings affirm that the asynchrony among the patches plays an important role in the survivability of a metapopulation. In order to demonstrate the model independence of the observed phenomenon, we perform a similar analysis for patches exhibiting Holling type II functional response. On the grounds of the obtained results, our work is expected to provide a better perception of the influence of dispersal arrangements on the global survivability of ecological networks.
The order parameter D versus the inactivation ratio p in the globally coupled network for different dispersal values of m with α = β = 1.0. The critical ratio p c at which D becomes zero increases with descending values of the dispersal rate.

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2012

R. V. Gomez-Acata, Lopez-Perez, P. A., Aguilar-Lopez, R., Maya-Yescas, R., Q Zeng, H. X., Dr. Biswambhar Rakshit, S. Banerjee, Aihara, K., Ramírez, J. P., Aguirre, A. A., Fey, R. H. B., Nijmeijer, H., Torres-Treviño, L., Rodriguez, A., Pisarchik, A. N., Martínez-Zérega, B. E., Castro, J., Alvarez, J., Huerta-Cuellar, G., Jaimes-Reátegui, R., Sevilla-Escoboza, R., García-López, J. H., López-Mancilla, D., Castañeda-Hernández, C. E., and Murguia, C., “IFAC PROCEEDINGS VOLUMES (IFAC-PAPERSONLINE)”, Chaos, vol. 203, p. 208, 2012.

2012

Dr. Biswambhar Rakshit, Soumitro Banerjee, and Kazuyuki Aihara, “Circle Like Strange Attractor in a Piecewise Smooth Map”, IFAC Proceedings Volumes, vol. 45, pp. 81 - 86, 2012.[Abstract]


We explore the dynamics of a piecewise linear normal form map under the condition that the map is contractive in one compartment and expansive in the other. In particular, we analyze the transition from a mode-locked periodic orbit to a chaotic orbit. It occurs through the following sequence: first homoclinic contact followed by homoclinic intersection, which is again followed by a second homoclinic contact. We have shown that after the second homoclinic contact, a circular-shaped strange attractor with an infinite number of non-smooth folds is created. The mechanism of this chaotic behavior is explained in terms of tangencies with the stable foliation of the saddle fixed point.

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2010

Dr. Biswambhar Rakshit, Manjul Apratim, and Soumitro Banerjee, “Bifurcation phenomena in two-dimensional piecewise smooth discontinuous maps”, Chaos: An Interdisciplinary Journal of Nonlinear Science , 2010.[Abstract]


In recent years the theory of border collision bifurcations has been developed for piecewise smooth maps that are continuous across the border and has been successfully applied to explain nonsmooth bifurcation phenomena in physical systems. However, there exist a large number of switching dynamical systems that have been found to yield two-dimensional piecewise smooth maps that are discontinuous across the border. In this paper we present a systematic approach to the problem of analyzing the bifurcation phenomena in two-dimensional discontinuous maps, based on a piecewise linear approximation in the neighborhood of the border. We first motivate the analysis by considering the bifurcations occurring in a familiar physical system-the static VAR compensator used in electrical power systems-and then proceed to formulate the theory needed to explain the bifurcation behavior of such systems. We then integrate the observed bifurcation phenomenology of the compensator with the theory developed in this paper. This theory may be applied similarly to other systems that yield two-dimensional discontinuous maps.

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2009

Dr. Biswambhar Rakshit and Soumitro Banerjee, “Existence of chaos in a piecewise smooth two-dimensional contractive map”, Physics Letters A, vol. 373, pp. 2922 - 2926, 2009.[Abstract]


Piecewise smooth maps occur in a variety of physical systems. We show that in a two-dimensional continuous map a chaotic orbit can exist even when the map is contractive (eigenvalues less than unity in magnitude) at every point in the phase space. In this Letter we explain this peculiar feature of piecewise smooth continuous maps.

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2007

Dr. Biswambhar Rakshit, A. Roy Chowdhury, and Papri Saha, “Parameter estimation of a delay dynamical system using synchronization in presence of noise”, Chaos, Solitons & Fractals, vol. 32, pp. 1278 - 1284, 2007.[Abstract]


A method of parameter estimation of a time delay chaotic system through synchronization is discussed. It is assumed that the observed data can always be effected with some white Gaussian noise. A least square approach is used to derive a system of differential equations which governs the temporal evolution of the parameters. These system of equations together with the coupled delay dynamical systems, when integrated, leads to asymptotic convergence to the value of the parameter along with synchronization of the two system variables. This method is quite effective for estimating the delay time which is an important characteristic feature of a delay dynamical system. The procedure is quite robust in the presence of noise.

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2005

Dr. Biswambhar Rakshit, Papri Saha, and Asesh Roy Chowdhury, “Chaos and Control in Nonlinear Bloch System”, arXiv preprint nlin/0501004, 2005.[Abstract]


The dynamics of two nonlinear Bloch systems is studied from the viewpoint of bifur- cation and a particular parameter space has been explored for the stability analysis based on stability criterion. This enables the choice of the desired unstable periodic orbit from the numerous unstable ones present within the attractor through the pro- cess of closed return pairs. A generalized active control method have been discussed for two Bloch systems arising from di erent initial conditions.

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2005

Dr. Biswambhar Rakshit, Papri Saha, and Asesh Roy Chowdhury, “Multiple Attractor in Newton -Leipnik System, Peak to Peak dynamics and Chaos Control”, arXiv preprint nlin/0501014, 2005.[Abstract]


The chaotic properties of Newton-Leipnik system are discussed from the view point of strange attractors. Previously, two strange attractors of this system were illustrated which occured from two different initial conditions under the same parameter condition. It is found that above system also exhibits multiple attractors under different parameter values but same initial condition and we have shown the existence of three other strange attractors with varying dimensionality under different parametric conditions. The properties of these attractors are then analyzed on the basis of Lyapunov exponents, power spectra, recurrence analysis and peak-to-peak dynamics. The peak-to-peak dynamics relies on the low dimensionality of the chaotic attractor and allows to approximately model the system. Peak-to-peak plot along with return-time plot are then effectively used to solve the optimal control problem of the system which reverts the system to a periodic situation.

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2005

Papri Saha, Dr. Biswambhar Rakshit, and A. Roy Chowdhury, “On the analysis of spatial chaos and Hopf bifurcation in an optical open flow”, Chaos, Solitons & Fractals, vol. 25, pp. 367 - 378, 2005.[Abstract]


Spatial chaos in a system of copropagating nonlinear beam, interacting mutually, is explored. The case of four beams belonging to two weakly degenerate mode in a multimode fibre is analysed. The modulation of the waves due to mutual energy exchange is shown to give rise to chaos. We characterize the chaos with the help of Lyapunov exponent and phase space analysis. The case of centre manifold with imaginary eigenvalue is separated with the help of normal form analysis, when the system is reduced to a two component one. The reduced problem is then analysed with the help of a tangent field diagram.

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Publication Type: Conference Paper

Year of Publication Title

2009

Dr. Biswambhar Rakshit and S. Banerjee, “Transition to chaos through wrinkling of mode locked tori in a piecewise smooth Map”, in National Conference on Nonlinear Systems & Dynamics, Saha Institute of Nuclear Physics, Kolkata, India, 2009.[Abstract]


In this work we numerically find out a scenario for the two frequency torus breakdown to chaos in a piecewise smooth map. We show possible topological alterations that take place during the transition to chaos.

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