混沌动力学
Multistable dynamical systems are ever-prevalent, used to model for example ecosystems, power grids, climate elements, neurons, and more. When perturbed, such systems may ``tip'' from one state of operation to another, often with abrupt,…
In this note we explore numerically the finite Bernoulli convolutions. We show that with a suitable choice of parameter, it might serve as a toy model for intermittent energy cascade in fully developed turbulence. We then show how the…
In multiscale chaotic systems, a basic closure question is how much of the unresolved fine scales is instantaneously determined by the resolved coarse scales on the attractor. In a Fourier description, we formalize this by asking, given a…
Price-based mean-field models of battery storage coordination usually assume that each agent responds to the true population-average charging power. Under that assumption, communication topology is irrelevant because the broadcast price…
We study properties of solutions, both evolving and equilibrium of the wave-kinetic equation describing ensembles of weak random waves governed by the Kadomstev-Petviashivli-I equations. The latter equation is integrable by the inverse…
We compute the Lyapunov spectrum of the finite Euler ensembles, compact arithmetic fixed points of the rescaled momentum-loop equation for freely decaying incompressible Navier--Stokes turbulence. At finite cutoff \(N\), the tangential…
We investigate the origin and distribution of antiperiodicity -- oscillations satisfying $x(t+T)=-x(t)$ -- in the periodically driven Duffing--Holmes oscillator, combining analytical arguments with extensive numerical exploration. We first…
The periodically forced Duffing--Holmes oscillator possesses a discrete symmetry under sign reversal of the coordinate combined with a half-period shift of the drive. When this symmetry is dynamically realized, the system supports…
We investigate how cooperative feedback shapes global oscillatory dynamics in a glycolysis model with product recycling and allosteric phosphofructokinase regulation. Using bifurcation theory and numerical continuation, we analyze the…
This work presents a comprehensive analysis of coupled stochastic van der Pol oscillators, a paradigm for understanding synchronization, bifurcations, and chaos in nonlinear systems subject to random fluctuations. The system comprises two…
Inspired by nonequilibrium phenomena in game dynamics and behavioral evidence on the impact of extreme events on decision making, we investigate the nonlinear dynamics of a discrete-time multiagent learning rule in population congestion…
We report stable, ballistic cycler orbits in the circular restricted three-body problem: periodic trajectories that alternately undergo temporary capture about each primary. We construct continuous families of symmetric cyclers from…
This paper investigates the stability and large post-critical dynamics of an inextensible spinning fluid-conveying pipe with pinned-roller supports. Replacing the pinned-pinned support of the extensible counterpart with a sliding support…
We study the impact of the coupling topology on the ability of various networked dynamical systems to generate extreme events. By determining the coupling strength that is necessary to generate an extreme event in the collective dynamics of…
This work presents the mathematical modeling and numerical investigation of a thermo-controlled Micro-Electro-Mechanical System (MEMS) obtained by coupling an HP memristor with mechanical and electrical resonators. Using the linear drift HP…
We consider conformation dynamics of a chain-like three-body bead-spring model, in which three point masses are connected in series by two springs and the conformation is defined by the bending angle between the two springs. Previous…
We consider systems characterized by the presence of a rapidly oscillating force. A general method is presented for the construction of the effective action governing the large-scale nonlinear dynamics of such systems order by order in…
In this work, we study a family of fully chaotic billiards that exhibits only rotational symmetries, whose geometry is based on the $C_3$ symmetry system proposed by Leyvraz, Schmit, and Seligman~(LSS) in 1996. Quantum spectral analyses are…
We investigate the dynamical and analytical consequences of truncating the Gr\"unwald--Letnikov memory term in a fractional Duffing oscillator. The truncated memory is treated not merely as a computational approximation, but as a…
Complex-valued bidirectional associative memory (BAM) neural networks with fractional-order dynamics and delays can exhibit transient instabilities that degrade synchronization and short-horizon predictability. This paper develops a unified…