Ph.D, MSc, BSc

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.


Publication Type: Journal Article

Year of Publication Title


S. Kundu, Majhi, S., karmakar, P., Ghosh, D., and Dr. Biswambhar Rakshit, “Augmentation of dynamical persistence in networks through asymmetric interaction”, EPL (Europhysics Letters), vol. 123, no. 3, pp. 30001-p1 to 30001-p7, 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.

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S. Kundu, Majhi, S., Sasmal, S. Kumar, Ghosh, D., and Dr. Biswambhar Rakshit, “Survivability of a metapopulation under local extinctions”, Physical Review E, vol. 97, pp. 062212-1 to 062212-13, 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.

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Dr. Biswambhar Rakshit, Banerjee, S., and Aihara, K., “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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Dr. Biswambhar Rakshit, Apratim, M., and Banerjee, S., “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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Dr. Biswambhar Rakshit and Banerjee, S., “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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Dr. Biswambhar Rakshit, A. Chowdhury, R., and Saha, P., “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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P. Saha, Dr. Biswambhar Rakshit, and A. Chowdhury, R., “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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