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In this paper we study the controllability of networked systems with static network topologies using tools from algebraic graph theory. Each agent in the network acts in a decentralized fashion by updating its state in accordance with a…
Point-gap topology, characterized by spectral winding numbers, is crucial to non-Hermitian topological phases and dramatically alters real-time dynamics. In this paper, we study the evolution of quantum particles in dissipative systems with…
A nonsmooth fold is where an equilibrium or limit cycle of a nonsmooth dynamical system hits a switching manifold and collides and annihilates with another solution of the same type. We show that beyond the bifurcation the leading-order…
A salient feature of topological phases are surface states and many of the widely studied physical properties are directly tied to their existence. Although less explored, a variety of topological phases can however similarly be…
The analysis of global dynamics, particularly the identification and characterization of attractors and their regions of attraction, is essential for complex nonlinear and hybrid systems. Combinatorial methods based on Conley's index theory…
We analyze the coherent dynamics of excitons in three dimensional topologically disordered networks with traps. If the interactions between the nodes of the network are long ranged, i.e., algebraically decaying as a function of the distance…
It is well known that the addition of noise to a multistable dynamical system can induce random transitions from one stable state to another. For low noise, the times between transitions have an exponential tail and Kramers' formula gives…
We present the emergence of topological phase transition in the minimal model of two dimensional rock-paper-scissors cycle in the form of a doublet chain. The evolutionary dynamics of the doublet chain is obtained by solving the…
We apply the slip-back mapping method of Titov et al. 2009 and Lionello et al. 2020 to a thermodynamic MHD simulation to track topological changes in the magnetic field at a range of temporal cadences. The method constitutes the logical…
The topological hypothesis claims that phase transitions in a classical statistical mechanical system are related to changes in the topology of the level sets of the Hamiltonian. So far, the study of this hypothesis has been restricted to…
In networked systems, the interplay between the dynamics of individual subsystems and their network interactions has been found to generate multistability in various contexts. Despite its ubiquity, the specific mechanisms and ingredients…
We provide a proof of a recently conjectured universal bound on current fluctuations in Markovian processes. This bound establishes a link between the fluctuations of an individual observable current, the cycle affinities driving the system…
Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
Totally asymmetric exclusion processes (TASEP) with open boundaries are known to exhibit moving shocks or delocalised domain walls (DDW) for sufficiently small equal injection and extraction rates. In contrast TASEPs in an inhomogeneous…
We investigate the dynamics of a quantum system subjected to a time-dependent and conditional resetting protocol. Namely, we ask: what happens when the unitary evolution of the system is repeatedly interrupted at random time instants with…
We evolve network topology of an asymmetrically connected threshold network by a simple local rewiring rule: quiet nodes grow links, active nodes lose links. This leads to convergence of the average connectivity of the network towards the…
How biological networks achieve robust control despite relying on imperfect, local information remains an important open question. Here, we identify thermodynamic constraints that can curtail non-equilibrium steady-state responses so…
This paper presents a non-minimal order dynamics model for many analysis, simulation, and control problems of constrained mechanical systems with switching topology by making use of linear projection operator. The distinct features of this…
The relaxation dynamics of zero range process (ZRP) has always been an interesting problem. In this study, we set up the relationship between ZRP and traps model, and investigate the slow dynamics of ZRP in the framework of traps model.…