A scheme is suggested of the parametric generator of chaotic oscillations with attractor represented by a kind of Smale-Williams solenoid that operates under a periodic sequence of pump pulses at two different frequencies. Simulation of chaotic dynamics using the software product Multisim is provided.
This paper is concerned with the Chaplygin sleigh with timevarying mass distribution (parametric excitation). The focus is on the case where excitation is induced by a material point that executes periodic oscillations in a direction transverse to the plane of the knife edge of the sleigh. In this case, the problem reduces to investigating a reduced system of two first-order equations with periodic coefficients, which is similar to various nonlinear parametric oscillators. Depending on the parameters in the reduced system, one can observe different types of motion, including those accompanied …
A suite of analytical and computational techniques based on symbolic representations of simple and complex dynamics, is further developed and employed to unravel the global organization of bi-parametric structures that underlie the emergence of chaos in a simplified resonantly coupled wave triplet system, known as the Rabinovich system. Bi-parametric scans reveal the stunning intricacy and intramural connections between homoclinic and heteroclinic connections, and codimension-2 Bykov T-points and saddle structures, which are the prime organizing centers of complexity of the bifurcation unfoldi…
The principle of constructing a new class of systems with hyperbolic chaotic attractors is proposed. It is based on using oscillators, the transfer of excitation between which is provided resonantly due to the difference in the frequencies of small and large oscillations by an integer number of times being accompanied by phase transformation according to Bernoulli nap. We consider a system with Smale-Williams attractor, which is based on two coupled Bonhoeffer-van der Pol oscillators. The oscillators manifest activity and suppression turn by turn. With appropriate selection of the modulation, …
Parametric Correlations of Phase Shifts and Statistics of Time Delays in Quantum Chaotic Scattering: Crossover between Unitary and Orthogonal Symmetries
A Kerr-nonlinear parametric oscillator (KPO) can generate a quantum superposition of two oscillating states, known as a Schrödinger cat state, via quantum adiabatic evolution, and can be used as a qubit for gate-based quantum computing and quantum annealing. In this work, we investigate complex dynamics, i.e., chaos, in two coupled nondissipative KPOs at a few-photon level. After showing that a classical model for this system is nonintegrable and consequently exhibits chaotic behavior, we provide quantum counterparts for the classical results, which are quantum versions of the Poincaré surface…
Geometric investigation of chaos unfolding in Hamiltonian systems
Università di Padova（帕多瓦大学）；Istituto Nazionale di Ottica (INO) del Consiglio Nazionale delle Ricerche (CNR)（意大利国家研究委员会光学研究所）；Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；Consorzio RFX (CNR, ENEA, INFN, Università di Padova, Acciaierie Venete SpA)（RFX联盟）
In this paper, a two parameters family $F_{β_1,β_2}$ of maps of the plane living two different subspaces invariant is studied. We observe that, our model exhibits two chaotic attractors $A_i$, $i=0,1$, lying in these invariant subspaces and identify the parameters at which $A_i$ has a locally riddled basin of attraction or becomes a chaotic saddle. Then, the occurrence of riddled basin in the global sense is investigated in an open region of $β_1β_2$-plane. We semi-conjugate our system to a random walk model and define a fractal boundary which separates the basins of attraction of the two chao…
Distributed delays modeled by 'weak generic kernels' are introduced in the well-known coupled Landau-Stuart system, as well as a chaotic van der Pol-Rayleigh system with parametric forcing. The systems are close via the 'linear chain trick'. Linear stability analysis of the systems and conditions for Hopf bifurcation which initiates oscillations are investigated, including deriving the normal form at bifurcation, and deducing the stability of the resulting limit cycle attractor. The value of the delay parameter $a=a_{Hopf}$ at Hopf bifurcation picks out the onset of Amplitude Death(AD) in all …
Magnetostatic Spin Waves and Magnetic-Wave Chaos in Ferromagnetic Films. III. Numeric Simulations of Microwave-Band Magnetic Chaos, Its Synchronization and Application to Secure Communication
Integrable and Chaotic 4-Dimensional Lotka-Volterra Models and Population Sustainability
College of Health and Science, University of Lincoln（林肯大学健康与科学学院）；School of Computing and Digital Media, London Metropolitan University（伦敦城市大学计算与数字媒体学院）；Department of Electrical and Computer Engineering, University of Peloponnese（伯罗奔尼撒大学电气与计算机工程系）；Department of Mathematics, University of Patras（帕特雷大学数学系）
Optomechanical systems are known to exhibit a rich set of complex dynamical features including various types of chaotic behavior and multi-stability. Although this exotic behavior has attracted an intense research interest, the utilization of optomechanical systems in technological applications, in most cases necessitates a complex, yet predictable and controllable, oscillatory response. In fact, the various types of robust oscillations supported by optomechanical systems are nested in either the same or neighboring regions of the parameter space, where chaos exists. In this work we systematic…
We present a case study elaborating on the multiplicity and self-similarity of homoclinic and heteroclinic bifurcation structures in the 2D and 3D parameter spaces of a nonlinear laser model with a Lorenz-like chaotic attractor. In a symbiotic approach combining the traditional parameter continuation methods using MatCont and a newly developed technique called the Deterministic Chaos Prospector (DCP) utilizing symbolic dynamics on fast parallel computing hardware with graphics processing units (GPUs), we exhibit how specific codimension-two bifurcations originate and pattern regions of chaotic…
We theoretically describe the behavior of a terahertz nano-oscillator based on an anisotropic antiferromagnetic dynamical element driven by spin torque. We consider the situation when the polarization of the spin-current is perpendicular to the external magnetic field applied along the anisotropy easy-axis. We determine the domain of the parametric space (field, current) where the oscillator demonstrates chaotic dynamics. Characteristics of the chaotic regimes are analyzed using conventional techniques such as spectra of the Lyapunov exponents. We show that the threshold current of the chaos a…
Using the classical tools of nonlinear dynamics, we study the process of self-organization and the appearance of the chaos in the metabolic process in a cell with the help of a mathematical model of the transformation of steroids by a cell Arthrobacter globiformis. We constructed the phase-parametric diagrams obtained under a variation of the dissipation of the kinetic membrane potential. The oscillatory modes obtained are classified as regular and strange attractors. We calculated the bifurcations, by which the self-organization and the chaos occur in the system, and the transitions "chaos-or…
Bifurcation and chaos in the double well Duffing-van der Pol oscillator: Numerical and analytical studies
研究了驱动双阱Duffing-van der Pol（DVP）振荡器在特定参数选择（$\mid α\mid =β$）下的行为.在系统参数（$f-ω$）域中存在不同的吸引子进行检查和固定阻尼的各种稳定状态的详细说明。报道了通过混沌振荡从准周期运动到周期运动的转变。介入混沌制度进一步显示，具有岛屿的锁相状态和周期窗口（包括倍周期区域），边界危机，所有三个类的混沌，和瞬态混沌。我们还观察到在从拟周期解到周期解的过渡过程中存在间歇突变型的局部-全局分支和蓝天突变型的全局分支。利用微扰周期解，对各种形式的不稳定性进行了研究，可以预测$(f-ω)$平面上的Neimark不稳定性，并最终得到混沌区域的近似预测准则.
