Publications

@article{Wontchui2022,
title = {Intermingled attractors in an asymmetrically driven modified Chua oscillator},
author = {T T Wontchui and M E Sone and S R Ujjwal and J Y Effa and H P E Fouda and R Ramaswamy},
url = {https://pubs.aip.org/aip/cha/article/32/1/013106/2835551/Intermingled-attractors-in-an-asymmetrically},
doi = {10.1063/5.0069232},
issn = {1054-1500},
year = {2022},
date = {2022-01-03},
journal = {Chaos},
volume = {32},
number = {1},
abstract = {Understanding the asymptotic behavior of a dynamical system when system parameters are varied remains a key challenge in nonlinear dynamics. We explore the dynamics of a multistable dynamical system (the response) coupled unidirectionally to a chaotic drive. In the absence of coupling, the dynamics of the response system consists of simple attractors, namely, fixed points and periodic orbits, and there could be chaotic motion depending on system parameters. Importantly, the boundaries of the basins of attraction for these attractors are all smooth. When the drive is coupled to the response, the entire dynamics becomes chaotic: distinct multistable chaos and bistable chaos are observed. In both cases, we observe a mixture of synchronous and desynchronous states and a mixture of synchronous states only. The response system displays a much richer, complex dynamics. We describe and analyze the corresponding basins of attraction using the required criteria. Riddled and intermingled structures are revealed.},
keywords = {Chaos, Lorenz, Lyapunov exponent, Multistability},
pubstate = {published},
tppubtype = {article}
}

@article{Ujjwal2016a,
title = {Driving-induced multistability in coupled chaotic oscillators: Symmetries and riddled basins},
author = {Sangeeta Rani Ujjwal and Nirmal Punetha and Ram Ramaswamy and Manish Agrawal and Awadhesh Prasad},
url = {http://dx.doi.org/10.1063/1.4954022},
doi = {10.1063/1.4954022},
issn = {10541500},
year = {2016},
date = {2016-01-01},
journal = {Chaos},
volume = {26},
number = {6},
abstract = {The human brain, power grids, arrays of coupled lasers and the Amazon rainforest are all characterized by multistability. The likelihood that these systems will remain in the most desirable of their many stable states depends on their stability against significant perturbations, particularly in a state space populated by undesirable states. Here we claim that the traditional linearization-based approach to stability is too local to adequately assess how stable a state is. Instead, we quantify it in terms of basin stability, a new measure related to the volume of the basin of attraction. Basin stability is non-local, nonlinear and easily applicable, even to high-dimensional systems. It provides a long-sought-after explanation for the surprisingly regular topologies of neural networks and power grids, which have eluded theoretical description based solely on linear stability. We anticipate that basin stability will provide a powerful tool for complex systems studies, including the assessment of multistable climatic tipping elements.},
keywords = {Chaos, Multistability, Riddled Basins},
pubstate = {published},
tppubtype = {article}
}

@article{Kudrolli1994,
title = {Signatures of chaos in quantum billiards: Microwave experiments},
author = {A Kudrolli, S Sridhar, A Pandey and R Ramaswamy},
url = {https://link.aps.org/doi/10.1103/PhysRevE.49.R11},
doi = {10.1103/PhysRevE.49.R11},
year = {1994},
date = {1994-01-01},
journal = {Physical Review E},
volume = {49},
number = {1},
pages = {R11–R14},
abstract = {The signatures of classical chaos and the role of periodic orbits in the wave-mechanical eigenvalue spectra of two-dimensional billiards are studied experimentally in microwave cavities. The survival probability for all the chaotic cavity data shows a ‘‘correlation hole,’’ in agreement with theory, that is absent for the integrable cavity. The spectral rigidity
Δ
3
(L), which is a measure of long-range correlation, is shown to be particularly sensitive to the presence of marginally stable periodic orbits. Agreement with random-matrix theory is achieved only after excluding such orbits, which we do by constructing a special geometry, the Sinai stadium. Pseudointegrable geometries are also studied, and are found to display intermediate behavior.},
keywords = {Action-Billiard, Chaos, Quantum chaos},
pubstate = {published},
tppubtype = {article}
}

@article{Sinha1987b,
title = {On the dynamics of a controlled metabolic network and cellular behaviour},
author = {S Sinha and R Ramaswamy},
url = {https://www.sciencedirect.com/science/article/pii/0303264787900529},
doi = {10.1016/0303-2647},
issn = {0303-2647},
year = {1987},
date = {1987-01-26},
journal = {Biosystems},
volume = {20},
number = {4},
pages = {341-354},
abstract = {The existence of elaborate control mechanisms for the various biochemical processes inside and within living cells is responsible for the coherent behaviour observed in its spatio-temporal organisation. Stability and sensitivity are both necessary properties of living systems and these are achieved through negetive and positive feedback loops as in other control systems. We have studied a three-step reaction scheme involving a negative and a positive feedback loop in the form of end-product inhibition and allosteric activation. The variety of behaviour exhibited by this system, under different conditions, includes steady state, simple limit cycle oscillations, complex oscillations and period bifurcations leading to random oscillations or chaos. The system also shows the existence of two distinct chaotic regimes under the variation of a single parameter. These results, in comparison with single biochemical control loops, show that new behaviours can be exhibited in a more complex network which are not seen in the single control loops. The results are discussed in the light of a diverse variety of cellular functions in normal and altered cells indicating the role of controlled metabolic network as the underlying basis for cellular behaviour.},
keywords = {Chaos, Control},
pubstate = {published},
tppubtype = {article}
}

@article{Ramaswamy1983,
title = {Chaotic motions in vibrating molecules: The generalized Henon-Heiles model},
author = {Ramakrishna Ramaswamy},
url = {https://ramramaswamy.org/papers/018.pdf},
doi = {10.1016/0301-0104(83)85046-0},
issn = {03010104},
year = {1983},
date = {1983-01-01},
journal = {Chemical Physics},
volume = {76},
number = {1},
pages = {15–24},
abstract = {The method of avoided crossings is applied to a simple molecular model, the generalized Henon-Heiles system of coupled oscillators. The aim here is to determine the onset of wide-spread chaotic motions. The method is used to locate, in a simple manner, the resonances that lead to chaotic motions for different choices of parameters, wherein the frequencies of the unperturbed oscillators are in the ratio 3 : 4 and 7 : 13. The accuracy of the prediction is verified against numerical calculations of classical trajectories. textcopyright 1983.},
keywords = {Chaos, Henon-Heiles},
pubstate = {published},
tppubtype = {article}
}

@article{Ramaswamy1981b,
title = {The onset of chaotic motions in deterministic systems},
author = {R Ramaswamy and R A Marcus
},
url = {https://doi.org/10.1063/1.441202},
doi = {10.1063/1.441202},
issn = {0021-9606},
year = {1981},
date = {1981-01-15},
journal = {The Journal of Chemical Physics},
volume = {74},
number = {2},
pages = {1385–1393},
abstract = {In the present paper the classical counterpart of the quantum avoided crossing method for detecting chaos is described using classical (Lie‐transform) perturbation theory and a grid of action variables. The results are applied to two systems of coupled oscillators with cubic and quartic nonlinearities. The plots of energy of members of the grid versus the perturbation parameter provide a visual description for predicting the onset of chaos.},
keywords = {Chaos, Coupled Oscillators, Perturbation},
pubstate = {published},
tppubtype = {article}
}

@article{,
title = {Design strategies for generalized synchronization},
author = { },
url = { },
doi = { },
journal = { },
volume = { },
publisher = {American Physical Society},
abstract = { },
keywords = {Chaos, Coupled Lorenz System, Generalized Synchronization},
pubstate = {published},
tppubtype = {article}
}