We describe a peculiar type of spontaneous synchronization in a transmission line studded with nonlinear oscillators. After a transient period of complicated interactions, the elements form strongly synchronized pairs with interactions between these pairs virtually nil. The creation of these “dynamical dimers” appears to stem from the coupling intrinsic to transmission lines rather than any spe...

Partial network synchronization is studied for a class of nonlinear oscillators interconnected through diffusive dynamic couplings. We construct diffusive dynamic couplings combining nonlinear observers and output feedback controllers. Sufficient conditions on the systems to be interconnected, on the network topology, on the observer dynamics, and on the coupling strength that guarantee (global...

Quantitative characterization of nonlinear directional couplings between stochastic oscillators from data is considered. We suggest coupling characteristics readily interpreted from a physical viewpoint and their estimators. An expression for a statistical significance level is derived analytically that allows reliable coupling detection from a relatively short time series. Performance of the t...

In a recent paper [A. Yıldırım, Z. Saadatnia, H. Askari, “Application of the Hamiltonian approach to nonlinear oscillators with rational and irrational elastic terms”, Mathematical and Computer Modelling 54 (2011) 697-703] the so-called Hamiltonian approach (HA) was applied to obtain analytical approximate solutions for conservative nonlinear oscillators with certain elastic terms. In this pape...

We continue to study the arrays of nonlinear coupled oscillators. The networks of associative memory based on limit-cycle oscillators connected via complex-valued Hermitian matrices were previously designed. Another class of networks consisting of locally connected nonlinear oscillators, closely related to so-called cellular neural networks, is the subject of study in the present paper. In spat...

We demonstrate that nonidentical systems, in particular, nonlinear oscillators with different time scales, can be synchronized if a mutual coupling via time-delayed control signals is implemented. Each oscillator settles on an unstable state, say a fixed point or an unstable periodic orbit, with a coupling force which vanishes in the long time limit. We present the underlying theoretical consid...

Among control problems for mobile robots, point-to-point stabilization is the most challenging since it does not admit designs with smooth static state feedback laws. Stabilization strategies for mobile robots, and nonholonomic systems generally, are smooth, time-varying or nonsmooth, time-invariant. Time-varying control strategies are designed with umdamped linear oscillators but their fixed s...