Related papers: A phenomenological approach to normal form modelin…
Fifty years after the invention of the laser diode and fourty years after the report of the butterfly effect - i.e. the unpredictability of deterministic chaos, it is said that a laser diode behaves like a damped nonlinear oscillator. Hence…
The dynamics of a model, originally proposed for a type of instability in plastic flow, has been investigated in detail. The bifurcation portrait of the system in two physically relevant parameters exhibits a rich variety of dynamical…
Many dynamical systems of different complexity, e.g. 1D logistic map, the Lorentz equations, or real phenomena, like turbulent convection, show chaotic behaviour. Despite huge differences, the dynamical scenarios for these systems are…
We report in this paper a complete analytical study on the bifurcations and chaotic phenomena observed in certain second-order, non-autonomous, dissipative chaotic systems. One-parameter bifurcation diagrams obtained from the analytical…
We derive a mathematical model of a nematic electrolyte based on a variational formulation of nematodynamics. Extending our previous work, we consider a general setup which incorporates dielectric anisotropy of the liquid-crystalline matrix…
Recent studies have extensively explored chaotic dynamics in quantum optical systems through the mean-field approximation, which corresponds to an ideal, fluctuation-free scenario. However, the inherent sensitivity of chaos to initial…
We examine the Melnikov criterion for transition to chaos in case of a single degree of freedom nonlinear oscillator with the Ueda well potential and an external periodic excitation term. Using effective Hamiltonian we have examined…
We analyze the origin and properties of the chaotic dynamics of two atomic ensembles in a driven-dissipative experimental setup, where they are collectively damped by a bad cavity mode and incoherently pumped by a Raman laser. Starting from…
We study a simple lattice model of shear-induced clustering in two dimensions in which clusters of particles aggregate under an imposed shear flow and fragment stochastically. Two non-equilibrium steady states are identified: an unjammed…
The crystallographic restriction theorem constrains two-dimensional nematicity to display either Ising ($Z_{2}$) or three-state-Potts ($Z_{3}$) critical behaviors, both of which are dominated by amplitude fluctuations. Here, we use group…
We consider coupled slow-fast stochastic processes, where the averaged slow motion is given by a two-dimensional Hamiltonian system with multiple critical points. On a proper time scale, the evolution of the first integral converges to a…
The field of active nematics has traditionally employed descriptions based on dipolar activity, with interactions that align along a single axis. However, it has been theoretically predicted that interactions with a substrate, prevalent in…
In tokamak plasmas, sheared flows perpendicular to the driving temperature gradients can strongly stabilize linear modes. While the system is linearly stable, regimes with persistent nonlinear turbulence may develop, i.e. the system is…
We examine fluctuation-induced (pseudo-Casimir) interactions in nematic liquid-crystalline films confined between two surfaces, where one of the surfaces imposes a strong homeotropic anchoring (ensuring a uniform mean director profile),…
Nonlinearities in constitutive equations of extended objects in shear flow lead to novel phenomena, {\it e.g.} "rheochaos" in solutions of wormlike micelles and "elastic turbulence" in polymer solutions. Since both phenomena involve…
Bouncing droplets on a vibrating fluid bath can exhibit wave-particle behavior, such as being propelled by interacting with its own wave field. These droplets seem to walk across the bath, and thus are dubbed walkers. Experiments have shown…
Microresonators are micron-scale optical systems that confine light using total internal reflection. These optical systems have gained interest in the last two decades due to their compact sizes, unprecedented measurement capabilities, and…
We study the kinetics of the nematic-isotropic transition in a two-dimensional liquid crystal by using a lattice Boltzmann scheme that couples the tensor order parameter and the flow consistently. Unlike in previous studies, we find the…
In this paper we revisit the Mackey-Glass model for blood-forming process, which was proposed to describe the spontaneous fluctuations of the blood cell counts in normal individuals and the first stage of chronic myelocytic (or…
We prove the presence of chaos near a homoclinic orbit in the modified Li-Yorke sense [10] by implementing chaotic perturbations. A Duffing oscillator is considered to show the effectiveness of our technique, and simulations that support…