Jane Sheeba - Academia.edu (original) (raw)
Papers by Jane Sheeba
Applied Mathematics and Computation, Nov 1, 2013
In this paper, we present a method to identify integrable complex nonlinear oscillator systems an... more In this paper, we present a method to identify integrable complex nonlinear oscillator systems and construct their solutions. For this purpose, we introduce two types of nonlocal transformations which relate specific classes of nonlinear complex ordinary differential equations (ODEs) with complex linear ODEs, thereby proving the integrability of the former. We also show how to construct the solutions using the two types of nonlocal transformations with several physically interesting cases as examples.
Physics Letters A, 2012
Existence of amplitude independent frequencies of oscillation is an unusual property for a nonlin... more Existence of amplitude independent frequencies of oscillation is an unusual property for a nonlinear oscillator. We find that a class of N coupled nonlinear Liénard type oscillators exhibit this interesting property. We show that a specific subset can be explicitly solved from which we demonstrate the existence of periodic and quasiperiodic solutions. Another set of N-coupled nonlinear oscillators, possessing the amplitude independent nature of frequencies, is almost integrable in the sense that the system can be reduced to a single nonautonomous first order scalar differential equation which can be easily integrated numerically .
We have identified the existence of globally clustered chimera states in delay coupled oscillator... more We have identified the existence of globally clustered chimera states in delay coupled oscillator populations and find that these states can breathe periodically, aperiodically and become unstable depending upon the value of coupling delay. We also find that the coupling delay induces frequency suppression in the desynchronized group. We provide numerical evidence and theoretical explanations for the above results and discuss possible applications of the observed phenomena.
Biophysical Journal, Sep 1, 2008
There is growing evidence in favour of the temporal-coding hypothesis that temporal correlation o... more There is growing evidence in favour of the temporal-coding hypothesis that temporal correlation of neuronal discharges may serve to bind distributed neuronal activity into unique representations and, in particular, that θ (3.5-7.5 Hz) and δ (0.5 <3.5 Hz) oscillations facilitate information coding. The θ and δ rhythms are shown to be involved in various sleep stages, and during anaesthesia, and they undergo changes with the depth of anaesthesia. We introduce a thalamocortical model of interacting neuronal ensembles to describe phase relationships between θ and δ oscillations, especially during deep and light anaesthesia. Asymmetric and long range interactions among the thalamocortical neuronal oscillators are taken into account. The model results are compared with the experimental observations of Musizza et al. J. Physiol. (London) 2007 580:315-326. The δ and θ activities are found to be separately generated and are governed by the thalamus and cortex respectively. Changes in the degree of intra-ensemble and interensemble synchrony imply that the neuronal ensembles inhibit information coding during deep anaesthesia and facilitate it during light anaesthesia.
Journal of Physics A Mathematical and General
We explore a nonlocal connection between certain linear and nonlinear ordinary differential equat... more We explore a nonlocal connection between certain linear and nonlinear ordinary differential equations (ODEs), representing physically important oscillator systems, and identify a class of integrable nonlinear ODEs of any order. We also devise a method to derive explicit general solutions of the nonlinear ODEs. Interestingly, many well known integrable models can be accommodated into our scheme and our procedure thereby provides further understanding of these models.
Physical Review Letters
We seek explanation for the neurophysiological phenomenon of event related desynchronization (ERD... more We seek explanation for the neurophysiological phenomenon of event related desynchronization (ERD) by using models of diffusively coupled nonlinear oscillators. We demonstrate that when the strength of the event is sufficient, ERD is found to emerge and the accomplishment of a behavioral/functional task is determined by the nature of the desynchronized state. We illustrate the phenomenon for the case of limit cycle and chaotic systems. We numerically demonstrate the occurrence of ERD and provide analytical explanation. We also discuss possible applications of the observed phenomenon in real physical systems other than the brain.
Physical Review E
We report that asymmetrically interacting ensembles of oscillators follow novel routes to synchro... more We report that asymmetrically interacting ensembles of oscillators follow novel routes to synchrony. These routes seem to be a characteristic feature of coupling asymmetry. We show that they are unaffected by white noise except that the entrainment frequencies are shifted. The probability of occurrence of the routes is determined by phase asymmetry. The identification of these phenomena offers new insight into synchrony between oscillator ensembles and suggest new ways in which it may be controlled.
Evolution of quantum fidelity for two-level systems is studied in the context of periodic echo. F... more Evolution of quantum fidelity for two-level systems is studied in the context of periodic echo. From a general treatment for time independent case, we obtain a simple condition on the governing Hamiltonians under which the systems display periodic quantum echo. For a specific time dependent problem the quantum fidelity is shown to exhibit Rabi oscillation. This may be considered as a simple mechanism to generate periodic echo, except for a specific initial superpositional state in which case the fidelity remains invariant.
Physica D Nonlinear Phenomena
Adaptive coupling, where the coupling is dynamical and depends on the behaviour of the oscillator... more Adaptive coupling, where the coupling is dynamical and depends on the behaviour of the oscillators in a complex system, is one of the most crucial factors to control the dynamics and streamline various processes in complex networks. In this paper, we have demonstrated the occurrence of multi-stable states in a system of identical phase oscillators that are dynamically coupled. We find that the multi-stable state is comprised of a two cluster synchronization state where the clusters are in anti-phase relationship with each other and a desynchronization state. We also find that the phase relationship between the oscillators is asymptotically stable irrespective of whether there is synchronization or desynchronization in the system. The time scale of the coupling affects the size of the clusters in the two cluster state. We also investigate the effect of both the coupling asymmetry and plasticity asymmetry on the multi-stable states. In the absence of coupling asymmetry, increasing the...
Chaos Solitons & Fractals, 2007
Evolution of quantum fidelity for two-level systems is studied in the context of periodic echo. F... more Evolution of quantum fidelity for two-level systems is studied in the context of periodic echo. For time independent case, we obtain a formal condition on the governing Hamiltonians under which the systems display periodic quantum echo. In addition, a revisit of single spin-1/2 system exposed to uniform rotating magnetic field elucidates that the well known Rabi oscillation is a simple
Physical Review E, 2009
We have identified the existence of globally clustered chimera states in delay coupled oscillator... more We have identified the existence of globally clustered chimera states in delay coupled oscillator populations and find that these states can breathe periodically, aperiodically and become unstable depending upon the value of coupling delay. We also find that the coupling delay induces frequency suppression in the desynchronized group. We provide numerical evidence and theoretical explanations for the above results and discuss possible applications of the observed phenomena.
Physical Review E, 2011
We study the effect of coupling delay in a regular network with a ring topology and in a more com... more We study the effect of coupling delay in a regular network with a ring topology and in a more complex network with an all-to-all (global) topology in the presence of impurities (disorder). We find that the coupling delay is capable of inducing phase coherent chaotic oscillations in both types of networks thereby enhancing the spatiotemporal complexity even in the presence of 50% of symmetric disorders of both fixed and random types. Further, the coupling delay increases the robustness of the networks upto 70% of disorders, thereby preventing the network from acquiring periodic oscillations to foster disorder-induced spatiotemporal order. We also confirm the enhancement of coherent chaotic oscillations using snapshots of the phases and values of the associated Kuramoto order parameter. We also explain a possible mechanism for the phenomenon of delay-induced coherent chaotic oscillations despite the presence of large disorders and discuss its applications.
Chaos, 2010
Occurrence of strong or mass synchronization of a large number of neuronal populations in the bra... more Occurrence of strong or mass synchronization of a large number of neuronal populations in the brain characterizes its pathological states. In order to establish an understanding of the mechanism underlying such pathological synchronization, we present a model of coupled populations of phase oscillators representing the interacting neuronal populations. Through numerical analysis, we discuss the occurrence of mass synchronization in the
![Research paper thumbnail of Publisher's Note: Chimera and globally clustered chimera: Impact of time delay [Phys. Rev. E 81, 046203 (2010)]](https://a.academia-assets.com/images/blank-paper.jpg)
](Publisher&#x27;s Note: Chimera and globally clustered chimera: Impact of time delay [Phys... more Publisher&#x27;s Note: Chimera and globally clustered chimera: Impact of time delay [Phys. Rev. E 81, 046203 (2010)]. ...
Changes in the level of synchronization and desynchronization in coupled oscillator systems due t... more Changes in the level of synchronization and desynchronization in coupled oscillator systems due to an external stimulus is called event related synchronization or desynchronization (ERS/ERD). Such changes occur in real life systems where the collective activity of the entities of a coupled system is affected by some external influence. In order to understand the role played by the external influence in the occurrence of ERD and ERS, we study a system of coupled nonlinear oscillators in the presence of an external stimulus signal. We find that the phenomena of ERS and ERD are generic and occur in all types of coupled oscillator systems. We also find that the same external stimulus signal can cause ERS and ERD depending upon the strength of the signal. We identify the stability of the ERS and ERD states and also find analytical and numerical boundaries between the different synchronization regimes involved in the occurrence of ERD and ERS.
Evolution of quantum fidelity for two-level systems is studied in the context of periodic echo. F... more Evolution of quantum fidelity for two-level systems is studied in the context of periodic echo. From a general treatment for time independent case, we obtain a simple condition on the governing Hamiltonians under which the systems display periodic quantum echo. For a specific time dependent problem the quantum fidelity is shown to exhibit Rabi oscillation. This may be considered as a simple mechanism to generate periodic echo, except for a specific initial superpositional state in which case the fidelity remains invariant.
A system of two coupled ensembles of phase oscillators can follow different routes to inter-ensem... more A system of two coupled ensembles of phase oscillators can follow different routes to inter-ensemble synchronization. Following a short report of our preliminary results [Phys. Rev. E. 78, 025201(R) (2008)], we present a more detailed study of the effects of coupling, noise and phase asymmetries in coupled phase oscillator ensembles. We identify five distinct synchronization regions, and new routes to synchronization that are characteristic of the coupling asymmetry. We show that noise asymmetry induces effects similar to that of coupling asymmetry when the latter is absent. We also find that phase asymmetry controls the probability of occurrence of particular routes to synchronization. Our results suggest that asymmetry plays a crucial role in controlling synchronization within and between oscillator ensembles, and hence that its consideration is vital for modeling real life problems.
Following a short report of our preliminary results [Phys. Rev. E 79, 055203(R) (2009)], we prese... more Following a short report of our preliminary results [Phys. Rev. E 79, 055203(R) (2009)], we present a more detailed study of the effects of coupling delay in diffusively coupled phase oscillator populations. We find that coupling delay induces chimera and globally clustered chimera (GCC) states in delay coupled populations. We show the existence of multi-clustered states that act as link between the chimera and the GCC states. A stable GCC state goes through a variety of GCC states, namely periodic, aperiodic, long-and short-period breathers and becomes unstable GCC leading to global synchronization in the system, on increasing time delay. We provide numerical evidence and theoretical explanations for the above results and discuss possible applications of the observed phenomena.
Applied Mathematics and Computation, Nov 1, 2013
In this paper, we present a method to identify integrable complex nonlinear oscillator systems an... more In this paper, we present a method to identify integrable complex nonlinear oscillator systems and construct their solutions. For this purpose, we introduce two types of nonlocal transformations which relate specific classes of nonlinear complex ordinary differential equations (ODEs) with complex linear ODEs, thereby proving the integrability of the former. We also show how to construct the solutions using the two types of nonlocal transformations with several physically interesting cases as examples.
Physics Letters A, 2012
Existence of amplitude independent frequencies of oscillation is an unusual property for a nonlin... more Existence of amplitude independent frequencies of oscillation is an unusual property for a nonlinear oscillator. We find that a class of N coupled nonlinear Liénard type oscillators exhibit this interesting property. We show that a specific subset can be explicitly solved from which we demonstrate the existence of periodic and quasiperiodic solutions. Another set of N-coupled nonlinear oscillators, possessing the amplitude independent nature of frequencies, is almost integrable in the sense that the system can be reduced to a single nonautonomous first order scalar differential equation which can be easily integrated numerically .
We have identified the existence of globally clustered chimera states in delay coupled oscillator... more We have identified the existence of globally clustered chimera states in delay coupled oscillator populations and find that these states can breathe periodically, aperiodically and become unstable depending upon the value of coupling delay. We also find that the coupling delay induces frequency suppression in the desynchronized group. We provide numerical evidence and theoretical explanations for the above results and discuss possible applications of the observed phenomena.
Biophysical Journal, Sep 1, 2008
There is growing evidence in favour of the temporal-coding hypothesis that temporal correlation o... more There is growing evidence in favour of the temporal-coding hypothesis that temporal correlation of neuronal discharges may serve to bind distributed neuronal activity into unique representations and, in particular, that θ (3.5-7.5 Hz) and δ (0.5 <3.5 Hz) oscillations facilitate information coding. The θ and δ rhythms are shown to be involved in various sleep stages, and during anaesthesia, and they undergo changes with the depth of anaesthesia. We introduce a thalamocortical model of interacting neuronal ensembles to describe phase relationships between θ and δ oscillations, especially during deep and light anaesthesia. Asymmetric and long range interactions among the thalamocortical neuronal oscillators are taken into account. The model results are compared with the experimental observations of Musizza et al. J. Physiol. (London) 2007 580:315-326. The δ and θ activities are found to be separately generated and are governed by the thalamus and cortex respectively. Changes in the degree of intra-ensemble and interensemble synchrony imply that the neuronal ensembles inhibit information coding during deep anaesthesia and facilitate it during light anaesthesia.
Journal of Physics A Mathematical and General
We explore a nonlocal connection between certain linear and nonlinear ordinary differential equat... more We explore a nonlocal connection between certain linear and nonlinear ordinary differential equations (ODEs), representing physically important oscillator systems, and identify a class of integrable nonlinear ODEs of any order. We also devise a method to derive explicit general solutions of the nonlinear ODEs. Interestingly, many well known integrable models can be accommodated into our scheme and our procedure thereby provides further understanding of these models.
Physical Review Letters
We seek explanation for the neurophysiological phenomenon of event related desynchronization (ERD... more We seek explanation for the neurophysiological phenomenon of event related desynchronization (ERD) by using models of diffusively coupled nonlinear oscillators. We demonstrate that when the strength of the event is sufficient, ERD is found to emerge and the accomplishment of a behavioral/functional task is determined by the nature of the desynchronized state. We illustrate the phenomenon for the case of limit cycle and chaotic systems. We numerically demonstrate the occurrence of ERD and provide analytical explanation. We also discuss possible applications of the observed phenomenon in real physical systems other than the brain.
Physical Review E
We report that asymmetrically interacting ensembles of oscillators follow novel routes to synchro... more We report that asymmetrically interacting ensembles of oscillators follow novel routes to synchrony. These routes seem to be a characteristic feature of coupling asymmetry. We show that they are unaffected by white noise except that the entrainment frequencies are shifted. The probability of occurrence of the routes is determined by phase asymmetry. The identification of these phenomena offers new insight into synchrony between oscillator ensembles and suggest new ways in which it may be controlled.
Evolution of quantum fidelity for two-level systems is studied in the context of periodic echo. F... more Evolution of quantum fidelity for two-level systems is studied in the context of periodic echo. From a general treatment for time independent case, we obtain a simple condition on the governing Hamiltonians under which the systems display periodic quantum echo. For a specific time dependent problem the quantum fidelity is shown to exhibit Rabi oscillation. This may be considered as a simple mechanism to generate periodic echo, except for a specific initial superpositional state in which case the fidelity remains invariant.
Physica D Nonlinear Phenomena
Adaptive coupling, where the coupling is dynamical and depends on the behaviour of the oscillator... more Adaptive coupling, where the coupling is dynamical and depends on the behaviour of the oscillators in a complex system, is one of the most crucial factors to control the dynamics and streamline various processes in complex networks. In this paper, we have demonstrated the occurrence of multi-stable states in a system of identical phase oscillators that are dynamically coupled. We find that the multi-stable state is comprised of a two cluster synchronization state where the clusters are in anti-phase relationship with each other and a desynchronization state. We also find that the phase relationship between the oscillators is asymptotically stable irrespective of whether there is synchronization or desynchronization in the system. The time scale of the coupling affects the size of the clusters in the two cluster state. We also investigate the effect of both the coupling asymmetry and plasticity asymmetry on the multi-stable states. In the absence of coupling asymmetry, increasing the...
Chaos Solitons & Fractals, 2007
Evolution of quantum fidelity for two-level systems is studied in the context of periodic echo. F... more Evolution of quantum fidelity for two-level systems is studied in the context of periodic echo. For time independent case, we obtain a formal condition on the governing Hamiltonians under which the systems display periodic quantum echo. In addition, a revisit of single spin-1/2 system exposed to uniform rotating magnetic field elucidates that the well known Rabi oscillation is a simple
Physical Review E, 2009
We have identified the existence of globally clustered chimera states in delay coupled oscillator... more We have identified the existence of globally clustered chimera states in delay coupled oscillator populations and find that these states can breathe periodically, aperiodically and become unstable depending upon the value of coupling delay. We also find that the coupling delay induces frequency suppression in the desynchronized group. We provide numerical evidence and theoretical explanations for the above results and discuss possible applications of the observed phenomena.
Physical Review E, 2011
We study the effect of coupling delay in a regular network with a ring topology and in a more com... more We study the effect of coupling delay in a regular network with a ring topology and in a more complex network with an all-to-all (global) topology in the presence of impurities (disorder). We find that the coupling delay is capable of inducing phase coherent chaotic oscillations in both types of networks thereby enhancing the spatiotemporal complexity even in the presence of 50% of symmetric disorders of both fixed and random types. Further, the coupling delay increases the robustness of the networks upto 70% of disorders, thereby preventing the network from acquiring periodic oscillations to foster disorder-induced spatiotemporal order. We also confirm the enhancement of coherent chaotic oscillations using snapshots of the phases and values of the associated Kuramoto order parameter. We also explain a possible mechanism for the phenomenon of delay-induced coherent chaotic oscillations despite the presence of large disorders and discuss its applications.
Chaos, 2010
Occurrence of strong or mass synchronization of a large number of neuronal populations in the bra... more Occurrence of strong or mass synchronization of a large number of neuronal populations in the brain characterizes its pathological states. In order to establish an understanding of the mechanism underlying such pathological synchronization, we present a model of coupled populations of phase oscillators representing the interacting neuronal populations. Through numerical analysis, we discuss the occurrence of mass synchronization in the
Publisher&#x27;s Note: Chimera and globally clustered chimera: Impact of time delay [Phys... more Publisher&#x27;s Note: Chimera and globally clustered chimera: Impact of time delay [Phys. Rev. E 81, 046203 (2010)]. ...
Changes in the level of synchronization and desynchronization in coupled oscillator systems due t... more Changes in the level of synchronization and desynchronization in coupled oscillator systems due to an external stimulus is called event related synchronization or desynchronization (ERS/ERD). Such changes occur in real life systems where the collective activity of the entities of a coupled system is affected by some external influence. In order to understand the role played by the external influence in the occurrence of ERD and ERS, we study a system of coupled nonlinear oscillators in the presence of an external stimulus signal. We find that the phenomena of ERS and ERD are generic and occur in all types of coupled oscillator systems. We also find that the same external stimulus signal can cause ERS and ERD depending upon the strength of the signal. We identify the stability of the ERS and ERD states and also find analytical and numerical boundaries between the different synchronization regimes involved in the occurrence of ERD and ERS.
Evolution of quantum fidelity for two-level systems is studied in the context of periodic echo. F... more Evolution of quantum fidelity for two-level systems is studied in the context of periodic echo. From a general treatment for time independent case, we obtain a simple condition on the governing Hamiltonians under which the systems display periodic quantum echo. For a specific time dependent problem the quantum fidelity is shown to exhibit Rabi oscillation. This may be considered as a simple mechanism to generate periodic echo, except for a specific initial superpositional state in which case the fidelity remains invariant.
A system of two coupled ensembles of phase oscillators can follow different routes to inter-ensem... more A system of two coupled ensembles of phase oscillators can follow different routes to inter-ensemble synchronization. Following a short report of our preliminary results [Phys. Rev. E. 78, 025201(R) (2008)], we present a more detailed study of the effects of coupling, noise and phase asymmetries in coupled phase oscillator ensembles. We identify five distinct synchronization regions, and new routes to synchronization that are characteristic of the coupling asymmetry. We show that noise asymmetry induces effects similar to that of coupling asymmetry when the latter is absent. We also find that phase asymmetry controls the probability of occurrence of particular routes to synchronization. Our results suggest that asymmetry plays a crucial role in controlling synchronization within and between oscillator ensembles, and hence that its consideration is vital for modeling real life problems.
Following a short report of our preliminary results [Phys. Rev. E 79, 055203(R) (2009)], we prese... more Following a short report of our preliminary results [Phys. Rev. E 79, 055203(R) (2009)], we present a more detailed study of the effects of coupling delay in diffusively coupled phase oscillator populations. We find that coupling delay induces chimera and globally clustered chimera (GCC) states in delay coupled populations. We show the existence of multi-clustered states that act as link between the chimera and the GCC states. A stable GCC state goes through a variety of GCC states, namely periodic, aperiodic, long-and short-period breathers and becomes unstable GCC leading to global synchronization in the system, on increasing time delay. We provide numerical evidence and theoretical explanations for the above results and discuss possible applications of the observed phenomena.