We apply a semi-discrete in time relaxation scheme to a weakly damped forced nonlinear Schrödinger system. This provides us with a discrete infinite-dimensional dynamical system. We prove the existence of a global attractor for this dynamical system.

We study two dynamical systems for the motion of three planar charged particles with charges nj ∈ {±1}, j = 1, 2, 3. Both dynamical systems are parametric with a parameter α ∈ [0, 1] and have the same nonlinear terms. As α = 0, 1, the dynamical systems have no chaos. However, one dynamical system may create chaos as α varies from zero to one. This may provide an example to show that the homotop...

We propose a theory of how the speech gesture determines change in a functionally relevant variable of vocal tract state (e.g., constriction degree). A core postulate of the theory is that the gesture determines how the variable evolves in time independently of any executive time-keeper. That is, the theory involves intrinsic timing of speech gestures. We compare the theory against others in wh...

In this paper, a dynamical model-based SMC (Sliding Mode Control) is proposed fortrajectory tracking of a 3-RPS (Revolute, Prismatic, Spherical) parallel manipulator. With ignoring smallinertial effects of all legs and joints compared with those of the end-effector of 3-RPS, the dynamical model ofthe manipulator is developed based on Lagrange method. By removing the unknown Lagrange multipliers...

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Using tools from stochastic contraction theory, we show how the synchronization of nonlinear dynamical systems helps protect those systems from stochastic pertubations. These results open new perpectives for understanding the functional role of synchronization in neuronal networks.

We consider an asset-pricing model with wealth dynamics in a market populated by heterogeneous agents. By assuming that all agents belonging to the same group agree to share their wealth whenever an agent joins the group or leaves it , we develop an adaptive model which characterizes the evolution of wealth distribution when agents switch between different trading strategies. Two groups with he...

This note is focused on a novel technique in order to establish the boundedness in more regular spaces for global attractors of dissipative dynamical systems, without appealing to uniform-in-time estimates. As an application of the abstract result, the semigroup generated by the strongly damped wave equation utt −∆ut −∆u + φ(u) = f with critical nonlinearity is considered, whose attractor is sh...

A key feature of a general nonlinear partially hyperbolic dynamical system is the absence of differentiability of its invariant splitting. In this paper, we show that often partial derivatives of the splitting exist and the splitting depends smoothly on the dynamical system itself.

In this paper, we treat the class of nonlinear uncertain dynamic systems that was considered in [1, 5, 9, 10]. We consider continuous-time dynamical systems whose nominal part is linear and whose uncertain part is norm-bounded. We study the problems of state observation and obtaining stabilizing controller for uncertain nonlinear systems, where the uncertainties are characterized by known bounds.