相关论文: Covering Relations and Non-autonomous Perturbation…

Coexisting periodic solutions of a dynamical system describing nonlinear optical processes of the second-order are studied. The analytical results concern both the simplified autonomous model and the extended nonautonomous model, including…

Dynamical control of excitable biological systems is often complicated by the difficult and unreliable task of pre-control identification of unstable periodic orbits (UPOs). Here we show that, for both chaotic and nonchaotic systems, UPOs…

We propose a physical witness for dynamically detecting topological phase transitions (TPTs) via an experimentally observable out-of-time-order correlation (OTOC). The distinguishable OTOC dynamics appears in the topological trivial and…

We provide a constructive method designed in order to control the stability of a given periodic orbit of a general completely integrable system. The method consists of a specific type of perturbation, such that the resulting perturbed…

Physicists have argued that periodic orbit bunching leads to universal spectral fluctuations for chaotic quantum systems. To establish a more detailed mathematical understanding of this fact, it is first necessary to look more closely at…

Out-of-time-order correlators (OTOCs) are a standard measure of quantum chaos. Of the four operators involved, one pair may be regarded as a source and the other as a probe. A usual approach, applicable to large-$N$ systems such as the SYK…

The theory of scarring of eigenfunctions of classically chaotic systems by short periodic orbits is extended in several ways. The influence of short-time linear recurrences on correlations and fluctuations at long times is emphasized. We…

A successive continuation method for locating connecting orbits in parametrized systems of autonomous ODEs is considered. A local convergence analysis is presented and several illustrative numerical examples are given.

Topology and nonlinearity are deeply connected. However, whether topological effects can arise solely from the structure of nonlinear interaction terms, and the nature of the resulting topological phases, remain to large extent open…

Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in…

We prove that certain non-exact magnetic Hamiltonian systems on products of closed hyperbolic surfaces and with a potential function of large oscillation admit non-constant contractible periodic solutions of energy below the Ma\~n\'e…

Human social interactions are typically recorded as time-specific dyadic interactions, and represented as evolving (temporal) networks, where links are activated/deactivated over time. However, individuals can interact in groups of more…

We have developed a linearization method to investigate the subthreshold oscillatory behaviors in nonlinear autonomous systems. By considering firstly the neuronal system as an example, we show that this theoretical approach can predict…

Causal discovery is a data-driven paradigm for analyzing complex systems, while physics-based models, such as ordinary differential equations (ODEs), provide mechanistic structure for real-world dynamical processes. Integrating these…

Periodic orbits are among the simplest non-equilibrium solutions to dynamical systems, and they play a significant role in our modern understanding of the rich structures observed in many systems. For example, it is known that embedded…

Hamiltonian theory of hybrid quantum-classical systems is used to study dynamics of the classical subsystem coupled to different types of quantum systems. It is shown that the qualitative properties of orbits of the classical subsystem…

Natural orbital functional theory is considered for systems with one or more unpaired electrons. An extension of the Piris natural orbital functional (PNOF) based on electron pairing approach is presented, specifically, we extend the…

Small non-autonomous perturbations around an equilibrium of a nonlinear delayed system are studied. Under appropriate assumptions, it is shown that the number of $T$-periodic solutions lying inside a bounded domain $\Omega\subset \R^N$ is,…

Vortex coherent structures on arrays of nonlinear oscillators joined by weak links into topologically nontrivial two-dimensional discrete manifolds have been theoretically studied. A circuit of nonlinear electric oscillators coupled by…

Out-of-Time-Order Correlators (OTOCs) serve as a proxy for quantum information scrambling, which refers to the process where information stored locally disperses across the many-body degrees of freedom in a quantum system, rendering it…