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It is well known that, contrary to the autonomous case, the stability/instability of solutions of nonautonomous linear ordinary differential equations $x' = A(t) x$ is in no relation to the sign of the real parts of the eigenvalues of…
Stability and safety are critical properties for successful deployment of automatic control systems. As a motivating example, consider autonomous mobile robot navigation in a complex environment. A control design that generalizes to…
Spontaneous growth of long-wavelength deformations is a defining feature of active fluids with orientational order. We investigate the effect of biaxial rectangular confinement on the instability of initially shear-aligned 3D isotropic…
Many day-to-day activities require the dexterous manipulation of a redundant humanoid arm in complex 3D environments. However, position regulation of such robot arm systems becomes very difficult in presence of non-linear uncertainties in…
The inverse problem of designing component interactions to target emergent structure is fundamental to numerous applications in biotechnology, materials science, and statistical physics. Equally important is the inverse problem of designing…
Many physical systems can be modelled as parameter-dependent variational problems. In numerous cases, multiple equilibria co-exist, requiring the evaluation of their stability, and the monitoring of transitions between them. Generally, the…
In theoretical ecology, models describing the spatial dispersal and the temporal evolution of species having non-overlapping generations are often based on integrodifference equations. For various such applications the environment has an…
A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by…
In data-based control, dissipativity can be a powerful tool for attaining stability guarantees for nonlinear systems if that dissipativity can be inferred from data. This work provides a tutorial on several existing methods for data-based…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
Recently, there has been an increasing interest in using tools from dynamical systems to analyze the behavior of simple optimization algorithms such as gradient descent and accelerated variants. This paper strengthens such connections by…
The discrete-dipole approximation (DDA) is a flexible technique for computing scattering and absorption by targets of arbitrary geometry. In this paper we perform systematic study of various non-stationary iterative (conjugate gradient)…
We introduce a distributed control architecture for a class of heterogeneous, nonlinear dynamical agents moving in the "string" formation, while guaranteeing trajectory tracking, collision avoidance and the preservation of the formation's…
Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…
Instabilities driven by strong gradients appear in a wide variety of physical systems, including plasmas, neutral fluids, and self-gravitating systems. This work develops an analytic formulation to describe the transport structure and…
The paper describes a novel method for studying the stability of nonautonomous dynamical systems. This method based on the flow and divergence of the vector field with coupling to the method of Lyapunov functions. The necessary and…
Models of complex dynamical systems like the Earth's climate often involve large numbers of uncertain parameters. Comprehensive exploration of the parameter space is typically prohibitive due to excessive computational costs. Systematic…
The high-multiplicity exoplanet systems are generally more tightly packed when compared to the solar system. Such compact multi-planet systems are often susceptible to dynamical instability. We investigate the impact of dynamical…
Self-propelled particles can navigate complex environments, including viscous fluid interfaces with curved geometries. In this work, we study the emergent dynamics of a suspension of self-propelled particles confined to a stationary curved…
Fourth-order accurate compact schemes for variable coefficient convection diffusion equations are considered. A sufficient condition for the stability of the fully discrete problem is derived using a difference equation based approach. The…