Amplitude death (AD) is an emergent phenomenon whereby two or more autonomously oscillating systems completely lose their oscillations due to coupling. In this work, we study AD in nonlinear oscillators with mixed time-delayed coupling, which is a combination of instantaneous and time-delayed couplings. We find that the mixed time-delayed coupling favors the onset of AD for a larger set of para...

A system of nonlinear oscillators of an extended Van der Pol type was recently introduced [1] by the author. Under certain conditions the solutions of this system are attracted by the solutions of a nonlinear conservative system [1, 2], It has been proved in [2] that the latter system is integrable in the case of two oscillators. For three or more oscillators the question of integrability is op...

Amplitude death is the cessation of oscillations that occurs in coupled nonlinear systems when fixed points are stabilized as a consequence of the interaction. We show here that this phenomenon is very general: it occurs in nonlinearly coupled systems in the absence of parameter mismatch or time delay although time-delayed interactions can enhance the effect. Application is made to synaptically...

Systems of coupled oscillators may exhibit spontaneous dynamical formation of attractingsynchronized clusters with broken symmetry; this can be helpful in modelling various physicalprocesses. Analytical computation of the stability of synchronized cluster states is usually impos-sible for arbitrary nonlinear oscillators. In this paper we examine a particular class of strongly<lb...

In this report we present an elegant method to build and maintain an antiphase configuration of two nonlinear oscillators with different natural frequencies and dynamics described by the sinusoidal phase-reduced model. The antiphase synchronization is achieved using a common input that couples the oscillators and consists of a sequence of square pulses of appropriate amplitude and duration. Thi...

We propose a method to infer the coupling structure in networks of nonlinear oscillatory systems with multiple time scales. The method of partial phase synchronization allows us to infer the coupling structure for coupled nonlinear oscillators with one well-defined time scale. The case of oscillators with multiple time scales has remained a challenge until now. Here, we introduce partial recurr...

The modified differential transform method (MDTM), Laplace transform and Padé approximants are used to investigate a semi-analytic form of solutions of nonlinear oscillators in a large time domain. Forced Duffing and forced van der Pol oscillators under damping effect are studied to investigate semi-analytic forms of solutions. Moreover, solutions of the suggested nonlinear oscillators are obta...

Very recently, Yildirim et al. [1] applied the so-called Hamiltonian approach (HA) to obtain analytical approximate solutions for three well-known nonlinear oscillators. The authors mentioned that this approach is a kind of energy method with a vast application in conservative oscillatory systems, and they applied the approach to nonlinear oscillators with rational and irrational elastic terms....

An analytical approximate technique for conservative nonlinear oscillators is proposed. This method is a modification of the generalized harmonic balance method in which analytical approximate solutions have a rational form. This approach gives us not only a truly periodic solution but also the frequency of motion as a function of the amplitude of oscillation. Three truly nonlinear oscillators ...

Chaotic oscillators based on RC-elements and nonlinear amplifiers with sigmoid function only are discussed. The analysis of the structure a number of wellknown oscillators is carried out. On the basis of that analysis the structure of the oscillators which consist of RC–elements and op amps only and capable to show chaotic oscillations is suggested. Computer simulation of chaotic behavior of os...