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{Ujjwal2017,
title = {Emergence of chimeras through induced multistability},
author = {S R Ujjwal and N Punetha and A Prasad and R Ramaswamy},
url = {https://ramramaswamy.org/papers/165.pdf},
doi = {10.1103/PhysRevE.95.032203},
issn = {2470-0053},
year = {2017},
date = {2017-01-01},
journal = {Physical Review E},
volume = {95},
pages = {032203 },
abstract = {Chimeras, namely coexisting desynchronous and synchronized dynamics, are formed in an ensemble of identically coupled identical chaotic oscillators when the coupling induces multiple stable attractors, and further when the basins of the different attractors are intertwined in a complex manner. When there is coupling-induced multistability, an ensemble of identical chaotic oscillators—with global coupling, or also under the influence of common noise or an external drive (chaotic, periodic, or quasiperiodic)—inevitably exhibits chimeric behavior. Induced multistability in the system leads to the formation of distinct subpopulations, one or more of which support synchronized dynamics, while in others the motion is asynchronous or incoherent. We study the mechanism for the emergence of such chimeric states, and we discuss the generality of our results.},
keywords = {Chimeras, Multistability, Quasiperiodicity},
pubstate = {published},
tppubtype = {article}
}

@article{Wontchui2017,
title = {Coupled Lorenz oscillators near the Hopf boundary: Multistability, intermingled basins, and quasiriddling},
author = {T T Wontchui and J Y Effa and H P E Fouda and S R Ujjwal and R Ramaswamy },
url = {https://ramramaswamy.org/papers/166.pdf},
doi = {10.1103/PhysRevE.96.062203},
issn = {2470-0053},
year = {2017},
date = {2017-01-01},
journal = {Physical Review E},
volume = {96},
pages = {062203},
abstract = {textcopyright 2017 American Physical Society. We investigate the dynamics of coupled identical chaotic Lorenz oscillators just above the subcritical Hopf bifurcation. In the absence of coupling, the motion is on a strange chaotic attractor and the fixed points of the system are all unstable. With the coupling, the unstable fixed points are converted into chaotic attractors, and the system can exhibit a multiplicity of coexisting attractors. Depending on the strength of the coupling, the motion of the individual oscillators can be synchronized (both in and out of phase) or desynchronized and in addition there can be mixed phases. We find that the basins have a complex structure: the state that is asymptotically reached shows extreme sensitivity to initial conditions. The basins of attraction of these different states are characterized using a variety of measures and depending on the strength of the coupling, they are intermingled or quasiriddled.},
keywords = {Intermingled Basins, Lorenz, Multistability, Quasiriddling},
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{Punetha2015a,
title = {Bipartite networks of oscillators with distributed delays: Synchronization branches and multistability},
author = {Nirmal Punetha and Ramakrishna Ramaswamy and Fatihcan M Atay},
url = {https://ramramaswamy.org/papers/160.pdf},
doi = {10.1103/PhysRevE.91.042906},
issn = {15502376},
year = {2015},
date = {2015-01-01},
journal = {Physical Review E – Statistical, Nonlinear, and Soft Matter Physics},
volume = {91},
number = {4},
pages = {1–10},
abstract = {We study synchronization in bipartite networks of phase oscillators with general nonlinear coupling and distributed time delays. Phase-locked solutions are shown to arise, where the oscillators in each partition are perfectly synchronized among themselves but can have a phase difference with the other partition, with the phase difference necessarily being either zero or $pi$ radians. Analytical conditions for the stability of both types of solutions are obtained and solution branches are explicitly calculated, revealing that the network can have several coexisting stable solutions. With increasing value of the mean delay, the system exhibits hysteresis, phase flips, final state sensitivity, and an extreme form of multistability where the numbers of stable in-phase and antiphase synchronous solutions with distinct frequencies grow without bound. The theory is applied to networks of Landau-Stuart and Rossler oscillators and shown to accurately predict both in-phase and antiphase synchronous behavior in appropriate parameter ranges.},
keywords = {Bipartite Network, Multistability, Synchronization},
pubstate = {published},
tppubtype = {article}
}