混沌动力学
Branched flow can be observed when a laser beam is coupled into a soap film. This research theoretically explored the phenomenon through analogy between light wave and particles in form of Hamilton-Jacobian equation, further discussed the…
Extracting predictive models from nonlinear systems is a central task in scientific machine learning. One key problem is the reconciliation between modern data-driven approaches and first principles. Despite rapid advances in machine…
We investigate the long-term diffusion transport and chaos properties of single and coupled standard maps. We consider model parameters that are known to induce anomalous diffusion in the maps' phase spaces, as opposed to normal diffusion…
Stable periodic orbits in spiral galactic models that form families of precessing ellipses can create spiral density waves similar to those that are observed in real grand-design galaxies. We study the range in parameter space for which the…
The high-order synchronization was studied in systems driven by external force and in autonomous systems with proper frequency mismatch. Differing from the literature, in this article, we demonstrate the occurrence of high-order (1:2)…
The Lorenz system is a milestone model of nonlinear dynamic systems. However, we report in this Letter that important information of the global solutions in the parameter space may still miss: there is a series of cascade solutions in…
A system of three non-identical Josephson junctions connected via an RLC circuit is considered. The method of Lyapunov exponents charts is used, which makes it possible to identify the main types of dynamics of the system and to analyze the…
Kuramoto's original model describes the dynamics and synchronization behavior of a set of interacting oscillators represented by their phases. The system can also be pictured as a set of particles moving on a circle in two dimensions, which…
In open Hamiltonian systems, the escape from a bounded region of phase space according to an exponential decay law is frequently associated with the existence of hyperbolic dynamics in such a region. Furthermore, exponential decay laws…
In this paper we demonstrate the capability of the method of Lagrangian descriptors to unveil the phase space structures that characterize transport in high-dimensional symplectic maps. In order to illustrate its use, we apply it to a…
In this paper we present in detail Newton's method and its modification, based on the Continuous analog of Newton's method for computing periodic orbits of the planar three-body problem. The linear system at each step of the method is…
We study behaviour of trajectories near a type Z heteroclinic network which is a union of two cycles. Analytical and numerical studies indicate that attractiveness of this network can be associated with various kinds of dynamics in its…
In this paper we demonstrate a route to develop coherence in a system of non-driven oscillators. Here, the coherence is brought about via physical collisions through which the oscillators exchange energy. While coherence in the classical…
In this manuscript we show that a noise-activated escape phenomenon occurs in closed Hamiltonian systems. Due to the energy fluctuations generated by the noise, the isopotential curves open up and the particles can eventually escape in…
Invariant curves are generally closed curves in the Poincare's surface of section. Here we study an interesting dynamical phenomenon, first discovered by Binney et al. (1985) in a rotating Kepler potential, where an invariant curve of the…
Remote synchronization implies that oscillators interacting not directly but via an additional unit (hub) adjust their frequencies and exhibit frequency locking while the hub remains asynchronous. In this paper, we analyze the mechanisms of…
In this paper, we explore the dynamics of a Hamiltonian system after a double van der Waals potential energy surface degenerates into a single well. The energy of the system is increased from the bottom of the potential well up to the…
Infinitesimal perturbations in various systems showing spatiotemporal chaos (STC) evolve following the power laws of the Kardar-Parisi-Zhang (KPZ) universality class. While universal properties beyond the power-law exponents, such as…
In this paper, we study an excitable, biophysical system that supports wave propagation of nerve impulses. We consider a slow-fast, FitzHugh-Rinzel neuron model where only the membrane voltage interacts diffusively, giving rise to the…
Nonlinear dynamical systems with time delay are abundant in applications, but are notoriously difficult to analyse and predict because delay-induced effects strongly depend on the form of the nonlinearities involved, and on the exact way…