Chaos break and synchrony enrichment within Hindmarsh–Rose-type memristive neural models

Nonlinear Dynamics - The fluctuation of ions concentration across the cell membrane of neuron can generate a time varying electromagnetic field. Thus, memristors are used to realize the coupling...     

Stability of Gaussian-type soliton in the cubic–quintic nonlinear media with fourth-order diffraction and $$\mathcal {PT}$$ PT -symmetric potentials

Nonlinear Dynamics - We report on the existence and stability of Gaussian-type soliton in the nonlinear Schrödinger (NLS) equation with interplay of cubic–quintic nonlinearity,...     

Anomalous transport and diffusion phenomena induced by biharmonic forces in deformable potential systems

We study transport properties of an inertial Brownian motor which moves in a deformable Remoissenet-Peyrad periodic potential and is subjected to both a static bias force and time periodic driving biharmonic force. By modifying the shape of the potential, the anomalous transport is identified for a particular set of the system parameters. For a particular potential shape, the mean velocity of a particle is modified by going from negative to positive values according to the external bias force. These features also depend on both the biharmonic parameter and the phase-lag of two signals. A remarkable transition of the negative velocity depending on the shape of the potential is observed. We also focus on the efficiency of the motor and discuss velocity fluctuation. In addition, within selected system parameters, different types of diffusion particle such as subdiffusion, superdiffusion, normal diffusion, ballistic diffusion, hyperdiffusion and dispersionless transport phenomena are generated in the system.     

Wave Trains Generation in a Delayed Nonlinear Response of Bose-Einstein Condensates with Three-Body Interactions

We investigate the modulational instability of matter-wave condensates in a modified Gross-Pitaevskii equation which takes into account effects of the three-body interaction. This three-body interaction consists of a quintic term and an additional one representing the delayed nonlinear response of condensates which are trapped both in an attractive and a repulsive harmonic potentials. Our theoretical study uses a modified lens-type transformation and we obtain a modulational instability criterion, and an explicit growth rate. We show that the presence of the three-body interaction destabilizes the condensate, and enhances the appearance of instability in the condensate. Numerical experiments agree well with analytical predictions. Furthermore, our numerical simulations show that the three-body interaction modifies the symmetry of the trail of soliton chains created. The expulsive potential enhances the instability, while the attractive potential appears to soften the instability.     

Instability domain of Bose–Einstein condensates with quantum fluctuations and three-body interactions

Through a Gross–Pitaevskii equation comprising cubic, quartic, residual, and quintic nonlinearities, we examine the modulational instability (MI) of Bose–Einstein condensates at higher densities in the presence of quantum fluctuations. We obtain an explicit time-dependent criteria for the MI and the instability domains of the condensates. Solitons are generated by suitably exciting the MI, and their stability is analyzed. We find that quantum fluctuations can completely change the instability of condensates by reversing the nature of the effective two-body interactions. The interplay between three-body interactions and quantum fluctuations is shown. Numerical simulations performed agree with analytical predictions.     

Hopf bifurcations on invariant manifolds of a modified Fitzhugh–Nagumo model

Nonlinear Dynamics - In this paper, we investigate the nonlinear vibration of a metamaterial structure that consists of a rotating cantilever beam attached to a periodic array of...     

Ultrashort self-similar periodic waves and similaritons in an inhomogeneous optical medium with an external source and modulated coefficients

Nonlinear Dynamics - In this paper, we use the similarity transformation to reduce the generalized higher-order nonlinear Schrödinger equation with space- and time-modulated coefficients...     

Similarity solutions of three-dimensional boundary layer equations of non-Newtonian fluids

An analysis of possibility of finding similaarity solutions to the three-dimensional, steady, incompressible, boundary layer equations in rectangular co-ordinates for a power law fluid has been discussed in the literature. In the present paper a similarity analysis is made of the steady, three-dimensional, incompressible, Iaminar, boundary layer flow of all time independent non-Newtonian fluids. The important conclusion drawn from this analysis in that for a non-Newtonian fiuid of any model, a similarity solution exists for the fluid for which shearing stress and rate of strain can be related by an arbitrary continuous function.