Dynamics of nonlinear oscillator with transient feedback

Dixit, Shiva; Sharma, Amit; Prasad, Awadhesh; Shrimali, Manish Dev

doi:10.1007/s40435-019-00534-9

Cited by 7 publications

(2 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where, τ = τ /T ∈ [0, 1], τ is an active interaction time window and T (= 2π/ω) is an average time period of the oscillations of uncoupled system 21,34 . Here, interaction is active for τ period of time, while it is inactive during the time T − τ as defined in Eq.…”

Section: B Temporal Dynamic Interaction (Tdi)mentioning

confidence: 99%

Emergent rhythms in coupled nonlinear oscillators due to dynamic interactions

Dixit,

Chowdhury,

Prasad

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

The role of a new form of dynamic interaction is explored in a network of generic identical oscillators. The proposed design of dynamic coupling facilitates the onset of a plethora of asymptotic states including synchronous states, amplitude death states, oscillation death states, a mixed state (complete synchronized cluster and small amplitude desynchronized domain), and bistable states (coexistence of two attractors). The dynamical transitions from the oscillatory to death state are characterized using an average temporal interaction approximation, which agrees with the numerical results in temporal interaction. A first order phase transition behavior may change into a second order transition in spatial dynamic interaction solely depending on the choice of initial conditions in the bistable regime. However, this possible abrupt first order like transition is completely non-existent in the case of temporal dynamic interaction. Besides the study on periodic Stuart-Landau systems, we present results for paradigmatic chaotic model of Rössler oscillators and Mac-arthur ecological model.Population biology of ecological networks, person to person communication networks, brain functional networks, possibility of outbreaks and spreading of disease through human contact networks, to name but a few examples which attest to the importance of researches based on temporal interaction approach. Studies based on representating several complex systems as time-varying networks of dynamical units have been shown to be extremely beneficial in understanding real life processes. Surprisingly, in all the previous studies on time-varying interaction, death state receives little attention in a network of coupled oscillators. In addition, only a few studies on dynamic interaction have considered the proximity of the individual systems' trajectories in the context of their interaction. In this paper, we propose a simple yet effective dynamic interaction scheme among nonlinear oscillators, which is capable of relaxing the collective oscillatory dynamics towards the dynamical equilibrium under appropriate choices of parameters. The dynamics of coupled oscillators can show fascinating complex behaviors including various dynamical phenomena. A qualitative explanation of the numerical observation is validated through linear stability analysis and interestingly, a linear stability analysis is persued even when the system is time-dependent. An elaborate study is contemplated to reveal the influences of our proposed dynamic interaction in terms of all the network parameters.

show abstract

Section: B Temporal Dynamic Interaction (Tdi)mentioning

confidence: 99%

Emergent rhythms in coupled nonlinear oscillators due to dynamic interactions

Dixit,

Chowdhury,

Prasad

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…For numerical simulation, ∆ ∈ [0, 1] assigns the closed interval [global minima of the attractor, global minima of the attractor + ( global maxima of the attractor − global minima of the attractor) × ∆] as the mean field active region. Clearly, when ∆ tends to 0+, then neither of those N oscillators get the suitable opportunity to interact among each other and as a consequence, only self-negative feedback is activated [49]. Besides, the global all-to-all interaction is established through mean field diffusive coupling for ∆ → 1−.…”

mentioning

confidence: 99%

Dynamic interaction induced explosive death

Dixit¹,

Chowdhury²,

Ghosh³

et al. 2021

EPL

Self Cite

View full text Add to dashboard Cite

Most previous studies on coupled dynamical systems assume that all interactions between oscillators take place uniformly in time, but, in reality, this does not necessarily reflect the usual scenario. The heterogeneity in the timings of such interactions strongly influences the dynamical processes. Here, we introduce a time-evolving state-space-dependent coupling among an ensemble of identical coupled oscillators, where individual units are interacting only when the mean state of the system lies within a certain proximity of the phase space. They interact globally with mean-field diffusive coupling in a certain vicinity and behave like uncoupled oscillators with self-feedback in the remaining complementary subspace. Interestingly due to this occasional interaction, we find that the system shows an abrupt explosive transition from oscillatory to death state. Further, in the explosive death transitions, the oscillatory state and the death state coexist over a range of coupling strengths near the transition point. We explore our claim using Van der Pol, FitzHugh-Nagumo and Lorenz oscillators with dynamic mean field interaction. The dynamic interaction mechanism can explain sudden suppression of oscillations and concurrence of oscillatory and steady state in biological as well as technical systems.

show abstract

Enlarging the stable domain of controlled high-period oscillations with transient extended delayed feedback control

Zheng

Zhang

2021

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

Dynamics of nonlinear oscillator with transient feedback

Cited by 7 publications

References 33 publications

Emergent rhythms in coupled nonlinear oscillators due to dynamic interactions

Emergent rhythms in coupled nonlinear oscillators due to dynamic interactions

Dynamic interaction induced explosive death

Enlarging the stable domain of controlled high-period oscillations with transient extended delayed feedback control

Contact Info

Product

Resources

About