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A network of noisy bistable elements with global time-delayed couplings is considered. A dichotomous mean field model has recently been developed describing the collective dynamics in such systems with uniform time delays near the…
We consider the adaptive control problem for discrete-time, nonlinear stochastic systems with linearly parameterised uncertainty. Assuming access to a parameterised family of controllers that can stabilise the system in a bounded set within…
We design, characterize, and couple Boolean phase oscillators that include state-dependent feedback delay. The state-dependent delay allows us to realize an adjustable coupling strength, even though only Boolean signals are exchanged.…
Fixed effect estimators of nonlinear panel data models suffer from the incidental parameter problem. This leads to two undesirable consequences in applied research: (1) point estimates are subject to large biases, and (2) confidence…
We study prediction-assimilation systems, which have become routine in meteorology and oceanography and are rapidly spreading to other areas of the geosciences and of continuum physics. The long-term, nonlinear stability of such a system…
We introduce a method to identify phase equations that include $N$-body interactions for general coupled oscillators valid far beyond the weak coupling approximation. This strategy is an extension of the theory from [Park and Wilson, SIADS…
There are three key factors of a system of coupled oscillators that characterize the interaction among them: coupling (how to affect), delay (when to affect) and topology (whom to affect). For each of them, the existing work has mainly…
We study synchronization and noise-induced resonance phenomena in systems of globally coupled oscillators, each possessing finite inertia. The behavior of the order parameter, which measures collective synchronization of the system, is…
In this work, we consider a system of multidimensional wave equations coupled by velocities with one localized fractional boundary damping. First, using a general criteria of Arendt- Batty, by assuming that the boundary control region…
We study the existence and stability of synchronous solutions in a continuum field of non-locally coupled identical phase oscillators with distance-dependent propagation delays. We present a comprehensive stability diagram in the parameter…
Coupled oscillator networks show a complex interrelations between topological characteristics of the network and the nonlinear stability of single nodes with respect to large but realistic perturbations. We extend previous results on these…
To date, the instability of prognostic predictors in a sparse high dimensional model, which hinders their clinical adoption, has received little attention. Stable prediction is often overlooked in favour of performance. Yet, stability…
We consider the nonlinear Duffing oscillator in presence of fractional damping which is characteristic in different physical situations. The system is studied with a smaller and larger damping parameter value, that we call the underdamped…
We analyze stability of a system which contains an harmonic oscillator non-linearly coupled to its second harmonic, in the presence of a driving force. It is found that there always exists a critical amplitude of the driving force above…
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…
Nonreciprocal coupling can alter the transport properties of material media, producing striking phenomena such as unidirectional amplification of waves, boundary modes, or self-assembled pattern formation. It is responsible for nonlinear…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…
This study proposes a method for designing stabilizing suboptimal controllers for nonlinear stochastic systems. These systems include time-invariant stochastic parameters that represent uncertainty of dynamics, posing two key difficulties…
Phase control of parametric modulation in coupled oscillator networks enables sculpting of dynamical states with desired spatiotemporal symmetries. Symmetry-aware Floquet analysis successfully predicts such states in linear systems, but…
We consider a model where a population of diffusively coupled limit-cycle oscillators, described by the complex Ginzburg-Landau equation, interacts nonlocally via an inertial field. For sufficiently high intensity of nonlocal inertial…