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Kuramoto oscillators are widely used to explain collective phenomena in networks of coupled oscillatory units. We show that simple networks of two populations with a generic coupling scheme, where both coupling strengths and phase lags…
Intermittent switchings between weakly chaotic (laminar) and strongly chaotic (bursty) states are often observed in systems with high-dimensional chaotic attractors, such as fluid turbulence. They differ from the intermittency of a…
We developed a powerful computational approach to elaborate on onset mechanisms of deterministic chaos due to complex homoclinic bifurcations in diverse systems. Its core is the reduction of phase space dynamics to symbolic binary…
A new method of symbolic analysis based on finite discretization of velocity-curvature space is proposed. A minimum alphabet is introduced in a natural way, and a number of initial analytic measures are defined that make it possible to…
Recurrence in the phase space of complex systems is a well-studied phenomenon, which has provided deep insights into the nonlinear dynamics of such systems. For dissipative systems, characteristics based on recurrence plots have recently…
Following a recent work (briefly reviewed below) we consider temporal fluctuations in the reduced density matrix elements for a coupled system involving a pair of kicked rotors as also one made up of a pair of Harper Hamiltonians. These…
Motivated by the famous ink-drop experiment, where ink droplets are used to determine the chaoticity of a fluid, we propose an experimentally implementable method for measuring the scrambling capacity of quantum processes. Here, a system of…
We consider the computation of out-of-time-ordered correlators (OTOCs) in the fishnet theories, with a mass term added. These fields theories are not unitary. We compute the growth exponent, in the planar limit, at any value of the coupling…
What is chaos? Despite several decades of research on this ubiquitous and fundamental phenomenon there is yet no agreed-upon answer to this question. Recently, it was realized that all stochastic and deterministic differential equations,…
Dissipative partial differential equations that exhibit chaotic dynamics tend to evolve to attractors that exist on finite-dimensional manifolds. We present a data-driven reduced order modeling method that capitalizes on this fact by…
We present a rigorous reassessment of chaotic behavior in two-dimensional autonomous systems with singular or nonsmooth dynamics. For the Cummings-Dixon-Kaus (CDK) model, we show that blow-up regularization restores smoothness and renders…
There are insights of chaotic properties in economic systems and data. To prove the existence of chaotic dynamics, the establishment of a deterministic model is mandatory. A global modelling tool (GPoM) is used to search for mathematical…
Lorenz attractors are important objects in the modern theory of chaos. The reason from one side is that they are met in various natural applications (fluid dynamics, mechanics, laser dynamics, etc.). At the same time, Lorenz attractors are…
This study examines second-order dynamical systems incorporating Tikhonov regularization. It focuses on how nonlinearities induce bifurcations and chaotic dynamics. By using Lyapunov functions, bifurcation theory, and numerical simulations,…
We show that rather simple but non-trivial boundary conditions could induce the appearance of spatial chaos (that is stationary, stable, but spatially disordered configurations) in extended dynamical systems with very simple dynamics. We…
Dynamical Systems theory generally deals with fixed point iterations of continuous functions. Computation by Turing machine although is a fixed point iteration but is not continuous. This specific category of fixed point iterations can only…
We analyze the behavior of a relativistic particle moving under the influence of a uniform magnetic field and a stationary electrostatic wave. We work with a set of pulsed waves that allows us to obtain an exact map for the system. We also…
Spatiotemporal chaotic systems are difficult to characterize in a model-free manner because of their high dimensionality, strong nonlinearity, and sensitivity to initial conditions. Coupled map lattices, as a representative class of…
The R\"ossler System is one of the best known chaotic dynamical systems, exhibiting a plethora of complex phenomena - and yet, only a few studies tackled its complexity analytically. In this paper we find sufficient conditions for the…
Non-linear dynamics is not a usually covered topic in undergraduate physics courses. However, its importance within classical mechanics and the general theory of dynamical systems is unquestionable. In this work we show that this subject…