Related papers: A geometric Birkhoffian formalism for nonlinear RL…
The dynamics of two nonlinear Bloch systems is studied from the viewpoint of bifur- cation and a particular parameter space has been explored for the stability analysis based on stability criterion. This enables the choice of the desired…
Many nonlinear systems are described by eigenmodes with amplitude-dependent frequencies, interacting strongly whenever the frequencies become commensurate at internal resonances. Fast energy exchange via the resonances holds the key to rich…
We study non-interacting electrons in disordered materials which exhibit a spectral gap, in each of the ten Altland--Zirnbauer symmetry classes, in all space dimensions. We define an appropriate space of Hamiltonians and a topology on it so…
The collective behavior of the ensembles of coupled nonlinear oscillator is one of the most interesting and important problems in modern nonlinear dynamics. In this paper, we study rotational dynamics, in particular space-time structures,…
We investigate dynamics near Turing patterns in reaction-diffusion systems posed on the real line. Linear analysis predicts diffusive decay of small perturbations. We construct a "normal form" coordinate system near such Turing patterns…
By incorporating physical consistency as inductive bias, deep neural networks display increased generalization capabilities and data efficiency in learning nonlinear dynamic models. However, the complexity of these models generally…
We begin with a review of the statements of non-linear, linear and mode stability of autonomous dynamical systems in classical mechanics, using symplectic geometry. We then discuss what the phase space and the Hamiltonian of general…
Circuit topology refers to the arrangement of interactions between objects belonging to a linearly ordered object set. Linearly ordered set of objects are common in nature and occur in a wide range of applications in economics, computer…
Electrical circuits offer a unique platform to explore physical phenomena, from topology to non-Hermitian effects. Investigations of the fundamental properties of this metamaterial platform are crucial to distinguish observed/measured…
In this work we discuss the natural appearance of the Generalized Brackets in systems with non-involutive (equivalent to second class) constraints in the Hamilton-Jacobi formalism. We show how a consistent geometric interpretation of the…
It has been known in the robotics literature since about 1995 that, in polar coordinates, the nonholonomic unicycle is asymptotically stabilizable by smooth feedback, even globally. We introduce a modular design framework that selects the…
Nonlinear perturbation of Fuchsian systems are studied in a region including two singularities. It is proved that such systems are generally not analytically equivalent to their linear part (they are not linearizable) and the obstructions…
Recurrent neural networks have been extensively studied in the context of neuroscience and machine learning due to their ability to implement complex computations. While substantial progress in designing effective learning algorithms has…
Changing a circuit dynamically, without actually changing the hardware itself, is called reconfiguration, and is of great importance due to its manifold technological applications. Circuit reconfiguration appears to be a feature of the…
The theory of circuit quantum electrodynamics has successfully analyzed superconducting circuits on the basis of the classical Lagrangian, and the corresponding quantized Hamiltonian, describing these circuits. In many simplified versions…
Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…
For an attracting periodic orbit (limit cycle) of a deterministic dynamical system, one defines the isochron for each point of the orbit as the cross-section with fixed return time under the flow. Equivalently, isochrons can be…
Positive definiteness of a Hamiltonian expanded about an equilibrium point provides only a necessary condition for stability, a criterion known as Dirichlet's theorem. The reason that this criterion is not necessary for stability is because…
Invariant foliations are geometric structures for describing and understanding the qualitative behaviors of nonlinear dynamical systems. For stochastic dynamical systems, however, these geometric structures themselves are complicated random…
In the present work we explore resistive circuits where the individual resistors are arranged in fractal-like patterns. These circuits have some of the characteristics typically found in geometric fractals, namely self-similarity and scale…