publications | Manaoj Aravind, PhD

2023

Phys. Rev. Appl.
Noise-Aided Invertible Logic from Coupled Nonlinear Systems

K. Murali, Manaoj Aravind, and Sudeshna Sinha

Physical Review Applied, 2023

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Invertible logic is a powerful new unconventional computing paradigm, providing bidirectional operations between inputs and outputs. It has found applications in important critical problems, such as integer factorization and machine learning. Here we propose a network of interconnected nonlinear systems that serve as our probabilistic bits (“p-bits”) to implement invertible logic in the presence of a noise floor. In the forward (or directed) mode, the inputs are fixed in our network, yielding outputs in accordance with and, or, nand, and nor logic functions. In the reverse (inverted) mode the output is clamped in the network, and the input nodes fluctuate among all possible logical input values consistent with the different logic functions. So the system acts as a unique invertible logic circuit by exploiting the probabilistic transitions between the dynamical states of the coupled noisy nonlinear systems. Interestingly, both the directed and the inverted mode are most robust and reliable in an optimal band of moderate noise, reminiscent of stochastic resonance. The concept is verified in proof-of-principle electronic circuit experiments, demonstrating the robustness of the architecture and the potential of this idea to be realized in a wide range of physical situations.
@article{murali2023invertible, title = {Noise-Aided Invertible Logic from Coupled Nonlinear Systems}, author = {Murali, K. and Aravind, Manaoj and Sinha, Sudeshna}, journal = {Physical Review Applied}, volume = {20}, issue = {3}, pages = {034041}, numpages = {10}, year = {2023}, publisher = {American Physical Society}, doi = {10.1103/PhysRevApplied.20.034041}, }
AIP Chaos
On relaxation times of heteroclinic dynamics

Manaoj Aravind and Hildegard Meyer-Ortmanns

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2023

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Heteroclinic dynamics provide a suitable framework for describing transient dynamics such as cognitive processes in the brain. It is appreciated for being well reproducible and at the same time highly sensitive to external input. It is supposed to capture features of switching statistics between metastable states in the brain. Beyond the high sensitivity, a further desirable feature of these dynamics is to enable a fast adaptation to new external input. In view of this, we analyze relaxation times of heteroclinic motion toward a new resting state, when oscillations in heteroclinic networks are arrested by a quench of a bifurcation parameter from a parameter regime of oscillations to a regime of equilibrium states. As it turns out, the relaxation is underdamped and depends on the nesting of the attractor space, the size of the attractor’s basin of attraction, the depth of the quench, and the level of noise. In the case of coupled heteroclinic units, it depends on the coupling strength, the coupling type, and synchronization between different units. Depending on how these factors are combined, finite relaxation times may support or impede a fast switching to new external input. Our results also shed some light on the discussion of how the stability of a system changes with its complexity.
@article{Aravind2023inertia, author = {Aravind, Manaoj and Meyer-Ortmanns, Hildegard}, title = {{On relaxation times of heteroclinic dynamics}}, journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science}, volume = {33}, number = {10}, pages = {103138}, year = {2023}, issn = {1054-1500}, doi = {10.1063/5.0166803}, }
PRL

Synchronization through frequency shuffling

Manaoj Aravind, Vaibhav Pachaulee, Ishant Tiwari, and 2 more authors

(Manuscript in review) Physical Review Letters, 2023

2022

Phys. Rev. E
Regulating dynamics through intermittent interactions

Shiva Dixit, Manaoj Aravind, and P. Parmananda

Physcal Review E, 2022

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In this article we experimentally demonstrate an efficient scheme to regulate the behavior of coupled nonlinear oscillators through dynamic control of their interaction. It is observed that introducing intermittency in the interaction term as a function of time or the system state predictably alters the dynamics of the constituent oscillators. Choosing the nature of the interaction, attractive or repulsive, allows for either suppression of oscillations or stimulation of activity. Two parameters Δ and τ, that reign the extent of interaction among subsystems, are introduced. They serve as a harness to access the entire range of possible behaviors from fixed points to chaos. For fixed values of system parameters and coupling strength, changing Δ and τ offers fine control over the dynamics of coupled subsystems. We show this experimentally using coupled Chua’s circuits and elucidate their behavior for a range of coupling parameters through detailed numerical simulations.
@article{dixit2022regulating, title = {Regulating dynamics through intermittent interactions}, author = {Dixit, Shiva and Aravind, Manaoj and Parmananda, P.}, journal = {Physcal Review E}, volume = {106}, issue = {1}, pages = {014203}, numpages = {8}, year = {2022}, publisher = {American Physical Society}, doi = {10.1103/PhysRevE.106.014203}, }

2021

Phys. Rev. E
Emergent noise-aided logic through synchronization

Manaoj Aravind, P Parmananda, and Sudeshna Sinha

Physical Review E, 2021

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In this article, we present a dynamical scheme to obtain a reconfigurable noise-aided logic gate that yields all six fundamental two-input logic operations, including the xor operation. The setup consists of two coupled bistable subsystems that are each driven by one subthreshold logic input signal, in the presence of a noise floor. The synchronization state of their outputs robustly maps to two-input logic operations of the driving signals, in an optimal window of noise and coupling strengths. Thus the interplay of noise, nonlinearity, and coupling leads to the emergence of logic operations embedded within the collective state of the coupled system. This idea is manifested using both numerical simulations and proof-of-principle circuit experiments. The regions in parameter space that yield reliable logic operations were characterized through a stringent measure of reliability, using both numerical and experimental data.
@article{aravind2021emergent, title = {Emergent noise-aided logic through synchronization}, author = {Aravind, Manaoj and Parmananda, P and Sinha, Sudeshna}, journal = {Physical Review E}, volume = {104}, number = {6}, pages = {064207}, year = {2021}, publisher = {APS}, }
Phil. Trans. A
Construction of logic gates exploiting resonance phenomena in nonlinear systems

K Murali, S Rajasekar, V Manaoj Aravind, and 3 more authors

Philosophical Transactions of the Royal Society A, 2021

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A two-state system driven by two inputs has been found to consistently produce a response mirroring a logic function of the two inputs, in an optimal window of moderate noise. This phenomenon is called logical stochastic resonance (LSR). We extend the conventional LSR paradigm to implement higher-level logic architecture or typical digital electronic structures via carefully crafted coupling schemes. Further, we examine the intriguing possibility of obtaining reliable logic outputs from a noise-free bistable system, subject only to periodic forcing, and show that this system also yields a phenomenon analogous to LSR, termed Logical Vibrational Resonance (LVR), in an appropriate window of frequency and amplitude of the periodic forcing. Lastly, this approach is extended to realize morphable logic gates through the Logical Coherence Resonance (LCR) in excitable systems under the influence of noise. The results are verified with suitable circuit experiments, demonstrating the robustness of the LSR, LVR and LCR phenomena.
@article{murali2021construction, title = {Construction of logic gates exploiting resonance phenomena in nonlinear systems}, author = {Murali, K and Rajasekar, S and Aravind, V Manaoj and Kohar, Vivek and Ditto, WL and Sinha, Sudeshna}, journal = {Philosophical Transactions of the Royal Society A}, volume = {379}, number = {2192}, pages = {20200238}, year = {2021}, publisher = {The Royal Society Publishing}, }
AIP Chaos
Competitive interplay of repulsive coupling and cross-correlated noises in bistable systems

Manaoj Aravind, Sudeshna Sinha, and P Parmananda

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2021

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The influence of noise on synchronization has potential impact on physical, chemical, biological, and engineered systems. Research on systems subject to common noise has demonstrated that noise can aid synchronization, as common noise imparts correlations on the sub-systems. In our work, we revisit this idea for a system of bistable dynamical systems, under repulsive coupling, driven by noises with varying degrees of cross correlation. This class of coupling has not been fully explored, and we show that it offers new counter-intuitive emergent behavior. Specifically, we demonstrate that the competitive interplay of noise and coupling gives rise to phenomena ranging from the usual synchronized state to the uncommon anti-synchronized state where the coupled bistable systems are pushed to different wells. Interestingly, this progression from anti-synchronization to synchronization goes through a domain where the system randomly hops between the synchronized and anti-synchronized states. The underlying basis for this striking behavior is that correlated noise preferentially enhances coherence, while the interactions provide an opposing drive to push the states apart. Our results also shed light on the robustness of synchronization obtained in the idealized scenario of perfectly correlated noise, as well as the influence of noise correlation on anti-synchronization. Last, the experimental implementation of our model using bistable electronic circuits, where we were able to sweep a large range of noise strengths and noise correlations in the laboratory realization of this noise-driven coupled system, firmly indicates the robustness and generality of our observations.
@article{aravind2021competitive, title = {Competitive interplay of repulsive coupling and cross-correlated noises in bistable systems}, author = {Aravind, Manaoj and Sinha, Sudeshna and Parmananda, P}, journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science}, volume = {31}, number = {6}, pages = {061106}, year = {2021}, publisher = {AIP Publishing LLC}, }
EPJ-ST
Ethanol lamp: a simple, tunable flame oscillator and its coupled dynamics

Manaoj Aravind, Ishant Tiwari, Vishwa Vasani, and 3 more authors

The European Physical Journal Special Topics, 2021

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In this paper, we introduce a simple controllable experimental system that can exhibit rich dynamics. The setup comprises a sealed glass vial of ethanol with wicks immersed in it. The flame produced by such a lamp can show both steady combustion or oscillatory combustion (i.e. flickering) depending on the volume of fuel within and the number of wicks used in its construction. This tunability makes it a great model system to study the dynamics of flame oscillations and to explore emergent behaviour of coupled nonlinear oscillators in table-top experiments. In the present work, the behaviour of this system for different fuel volumes is explored and some typical phenomena reported in other experimental systems, viz. in-phase synchronization, anti-phase synchronization and amplitude death are demonstrated.
@article{aravind2021ethanol, title = {Ethanol lamp: a simple, tunable flame oscillator and its coupled dynamics}, author = {Aravind, Manaoj and Tiwari, Ishant and Vasani, Vishwa and Cruz, Jos{\'e}-Manuel and Vasquez, Desiderio A and Parmananda, P}, journal = {The European Physical Journal Special Topics}, pages = {1--6}, year = {2021}, publisher = {Springer Berlin Heidelberg} }

2020

NodyCon2019
Synchronized Hopping Induced by Interplay of Coupling and Noise

V Manaoj Aravind, K Murali, and Sudeshna Sinha

In Nonlinear Dynamics and Control, 2020

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We explore the behaviour of coupled bistable systems subject to noise from two independent uncorrelated noise sources, over a range of coupling and noise strengths. We find that the interplay of coupling and noise leads to the emergence of four behavioural regimes: no synchrony and no hopping; unsynchronized hopping; synchronized hopping; synchrony without hopping. We show the occurrence of this phenomenon in a variety of bistable systems including the synthetic genetic network model, in the presence of both uniform and Gaussian noise, indicating the generality of this phenomenon. Further, we experimentally verify the different regimes of behaviour in coupled bistable electronic circuits, thus establishing its robustness.
@inproceedings{10.1007/978-3-030-34747-5_33, author = {Aravind, V Manaoj and Murali, K and Sinha, Sudeshna}, editor = {Lacarbonara, Walter and Balachandran, Balakumar and Ma, Jun and Tenreiro Machado, J. A. and Stepan, Gabor}, title = {Synchronized Hopping Induced by Interplay of Coupling and Noise}, booktitle = {Nonlinear Dynamics and Control}, year = {2020}, publisher = {Springer International Publishing}, address = {Cham}, pages = {325--334}, isbn = {978-3-030-34747-5}, }

2019

PNLD2019
Implementation of noise-aided logic gates with memristive circuits

V Manaoj Aravind, K Murali, and Sudeshna Sinha

In Proceedings of the Conference on Perspectives in Nonlinear Dynamics, 2019

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We implement robust logic gates utilizing a second order autonomous memristive circuit in the presence of a noise floor. We find that extremely reliable operations are obtained in an optimal band of moderate noise, with both direct and complementary logic operations obtained in parallel. The system also has the capacity to morph between logic functions efficiently by a simple change of bias, laying the foundation for noise-aided reconfigurable logic gates. Lastly, we implement coupling induced logical stochastic resonance (LSR) on a coupled system of memristors, paving the path for the realization of multi-input logic gates without the need for separate adder circuits. All ideas are demonstrated explicitly through numerical simulations, as well as proof-of-principle circuit experiments. Thus, our results suggest that the memristive circuit offers a promising system to implement robust and flexible logic operations in noisy environments and may help expand the scope of memristive device-based memcomputing.
@inproceedings{aravind2020implementation, title = {Implementation of noise-aided logic gates with memristive circuits}, author = {Aravind, V Manaoj and Murali, K and Sinha, Sudeshna}, booktitle = {Proceedings of the Conference on Perspectives in Nonlinear Dynamics}, volume = {3}, pages = {0004}, year = {2019}, }

2018

Phys. Lett. A
Coupling induced logical stochastic resonance

Manaoj Aravind, K Murali, and Sudeshna Sinha

Physics Letters A, 2018

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In this work we will demonstrate the following result: when we have two coupled bistable sub-systems, each driven separately by an external logic input signal, the coupled system yields outputs that can be mapped to specific logic gate operations in a robust manner, in an optimal window of noise. So, though the individual systems receive only one logic input each, due to the interplay of coupling, nonlinearity and noise, they cooperatively respond to give a logic output that is a function of both inputs. Thus the emergent collective response of the system, due to the inherent coupling, in the presence of a noise floor, maps consistently to that of logic outputs of the two inputs, a phenomenon we term coupling induced Logical Stochastic Resonance. Lastly, we demonstrate our idea in proof of principle circuit experiments.
@article{aravind2018coupling, title = {Coupling induced logical stochastic resonance}, author = {Aravind, Manaoj and Murali, K and Sinha, Sudeshna}, journal = {Physics Letters A}, volume = {382}, number = {24}, pages = {1581--1585}, year = {2018}, publisher = {North-Holland}, }