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In this article, we present a brief overview of some of the recent progress made in identifying and generating finite dimensional integrable nonlinear dynamical systems, exhibiting interesting oscillatory and other solution properties,…
We focus on an interesting dissipative system found in a photonics system. In this dissipative system, we theoretically identified that robust causality is generated and as a result, it becomes possible to produce behavior that can be…
Optimal nonlinear damping control was recently introduced for the second-order SISO systems, showing some advantages over a classical PD feedback controller. This paper summarizes the main theoretical developments and properties of the…
The steady state motion of a folded pendulum has been studied using frequencies of drive that are mainly below the natural (resonance) frequency of the instrument. Although the free-decay of this mechanical oscillator appears textbook…
Nearest level modulation (NLM) is an attractive modulation method for its implementation simplicity in modular multilevel converter (MMC). However, it introduces significant voltage and current distortion when the number of submodules (SMs)…
A novel method for the numerical prediction of the slowly varying dynamics of nonlinear mechanical systems has been developed. The method is restricted to the regime of an isolated nonlinear mode and consists of a two-step procedure: In the…
Frequency responses of multi-degree-of-freedom mechanical systems with weak forcing and damping can be studied as perturbations from their conservative limit. Specifically, recent results show how bifurcations near resonances can be…
We apply the Proper Orthogonal Decomposition (POD) method for the efficient simulation of several scenarios undergone by Micro-Electro-Mechanical-Systems, involving nonlinearites of geometric and electrostatic nature. The former type of…
Nonlinear modal interactions in resonant systems govern a wide range of phenomena, with broad relevance across modern physics and engineering. Yet, experimentally determining the strength of nonlinear coupling in multimode resonators…
Structural health monitoring (SHM) is an essential engineering field aimed at ensuring the safety and reliability of civil infrastructures. This study proposes a methodology using multivariate variational mode decomposition (MVMD) for…
This paper presents a new improved nonlinear tracking differentiator (INTD) with hyperbolic tangent function in the state space system. The stability and convergence of the INTD are thoroughly investigated and proved. Through the error…
The analysis of dissipatively coupled oscillators is challenging and highly relevant in power grids. Standard mathematical methods are not applicable, due to the lack of network symmetry induced by dissipative couplings. Here we demonstrate…
The $B_N$-type Calogero-Sutherland-Moser system in one-dimension is shown to be equivalent to a set of decoupled oscillators by a similarity transformation. This result is used to show the connection of the $A_N$ and $B_N$ type models and…
Dynamic mode decomposition (DMD) is a popular data-driven framework to extract linear dynamics from complex high-dimensional systems. In this work, we study the system identification properties of DMD. We first show that DMD is invariant…
We investigate application of the nonlinearity management (NM, i.e., periodic variation of the strength of the inter-component repulsion) to the miscibility-immiscibility (MIM) transition across the critical point of a two-component BEC,…
Multi-body mechanical systems have rich internal dynamics, whose solutions can be exploited as efficient control targets. Yet, solutions non-trivially depend on system parameters, obscuring feasible properties for use as target…
Recent experiments on spin torque oscillators have revealed interactions between multiple magnetodynamic modes, including mode-coexistence, mode-hopping, and temperature-driven cross-over between modes. Initial multimode theory has…
We introduce Variational Latent Mode Decomposition (VLMD), a new algorithm for extracting oscillatory modes and associated connectivity structures from multivariate signals. VLMD addresses key limitations of existing Multivariate Mode…
Reliable numerical computation of quantum dynamics is a fundamental challenge when the long-ranged quantum entanglement plays essential roles as in the cases governed by quantum criticality in strongly correlated systems. Here we apply a…
The nonlinear sigma model (NLSM) epitomises a field-theoretical approach to (interacting) electrons in disordered media. These lectures are aimed at the audience who might have vaguely heard about its existence but know very little of what…