相关论文: Bifurcation structure of two Coupled Periodically …

We investigate the resonance behaviour in a system composed by n-coupled Duffing oscillators where only the first oscillator is driven by a periodic force, assuming a nearest neighbour coupling. We have derived the frequency-response…

Discrete fractional order chaotic systems extends the memory capability to capture the discrete nature of physical systems. In this research, the memristive discrete fractional order chaotic system is introduced. The dynamics of the system…

A flame exhibits a limit-cycle oscillation, which is called "flame flickering" or "puffing", in a certain condition. We investigated the bifurcation structure of the flame oscillation in both simulation and experiment. We performed a…

We analyze the collective dynamics of an ensemble of globally coupled, externally forced, identical mechanical oscillators with cubic nonlinearity. Focus is put on solutions where the ensemble splits into two internally synchronized…

A simple electronic circuit with a voltage controlled current source is investigated. The circuit exhibits rich dynamics upon varying the circuit elements such as L,C and R, and the control factor of the current source. Among several other…

We consider an ecological model consisting of two species of predators competing for their common prey with explicit interference competition. With a proper rescaling, the model is portrayed as a singularly perturbed system with one-fast…

Nonlinear isolated and coupled oscillators are extensively studied as prototypical nonlinear dynamics models. Much attention has been devoted to oscillator synchronization or the lack thereof. Here, we study the synchronization and…

We study the effects of time delayed linear and nonlinear feedbacks on the dynamics of a single Hopf bifurcation oscillator. Our numerical and analytic investigations reveal a host of complex temporal phenomena such as phase slips,…

In this set of lectures, we review briefly some of the recent developments in the study of the chaotic dynamics of nonlinear oscillators, particularly of damped and driven type. By taking a representative set of examples such as the…

On a two-dimensional circular domain, we analyze the formation of spatio-temporal patterns for a class of coupled bulk-surface reaction-diffusion models for which a passive diffusion process occurring in the interior bulk domain is linearly…

The behaviors of coupled oscillators, each of which has periodic motion with random natural frequency in the absence of coupling, are investigated. Some novel collective phenomena are revealed. At the onset of instability of the…

The inner structure of the attractor appearing when the Varley-Gradwell-Hassell population model bifurcates from regular to chaotic behaviour is studied. By algebraic and geometric arguments the coexistence of a continuum of neutrally…

The effect of decaying oscillatory perturbations on autonomous Hamiltonian systems in the plane with a stable equilibrium is investigated. It is assumed that perturbations preserve the equilibrium and satisfy a resonance condition. The…

We have applied the Melnikov criterion to examine a global homoclinic bifurcation and transition to chaos in a case of the Duffing system with nonlinear fractional damping and external excitation. Using perturbation methods we have found a…

We present an unfolding of the codimension-two scenario of the simultaneous occurrence of a discontinuous bifurcation and an Andronov-Hopf bifurcation in a piecewise-smooth, continuous system of autonomous ordinary differential equations in…

The appearance of infinitely-many period-doubling cascades is one of the most prominent features observed in the study of maps depending on a parameter. They are associated with chaotic behavior, since bifurcation diagrams of a map with a…

Complex dynamical systems may exhibit multiple steady states, including time-periodic limit cycles, where the final trajectory depends on initial conditions. With tuning of parameters, limit cycles can proliferate or merge at an exceptional…

We address two aspects of the dynamics of the forced Duffing oscillator which are relevant to the technology of micromechanical devices and, at the same time, have intrinsic significance to the field of nonlinear oscillating systems. First,…

The asymmetrically forced, damped Duffing oscillator is introduced as a prototype model for analyzing the homoclinic tangle of symmetric dissipative systems with \textit{symmetry breaking} disturbances. Even a slight fixed asymmetry in the…

A density oscillator exhibits limit-cycle oscillations driven by the density difference of the two fluids. We performed two-dimensional hydrodynamic simulations with a simple model, and reproduced the oscillatory flow observed in…