Ters-Paralel Bağlı Schottky Diyot Dizisi Tabanlı Van der Pol Osilatörü Devresinin Modellenmesi ve LTspice ve Simulink Kullanarak Analizi

Van der Pol Osilatörü 1926 yılında, Philips’te çalışan elektrik mühendisi ve fizikçi Dr. Balthasar Van der Pol tarafından keşfedilmiştir. Bu osilatör çeşidinin oldukça zengin dinamikleri mevcuttur. İlk yapılan Van der Pol Osilatörü’nde bir triyot kullanılmıştır. Günümüzde Van der Pol Osilatörü, farklı yarı iletken elemanları kullanılarak yapılabilmektedir. Bu çalışmada, nonlineer devre elemanı olarak Schottky diyotlar kullanılmıştır. Bir endüktör, bir kondansatör, ters-paralel bağlı Schottky diyot dizisi ve paralel bağlanmış negatif direnç devresinden oluşan bu yeni Van der Pol Osilatörü’nün devre denklemleri türetilmiş ve benzetimi yapılarak incelenmiştir. Benzetimlerde devrenin sınır döngüsü, devre elemanlarının akımları ve devrenin gerilimi LTspice devre analizi programı ve Matlab’in Simulink paket programı kullanılarak elde edilmiştir

Saddle-Node bifurcations in classical and memristive circuits

This paper addresses a systematic characterization of saddle-node bifurcations in nonlinear electrical and electronic circuits. Our approach is a circuit-theoretic one, meaning that the bifurcation is analyzed in terms of the devices’ characteristics and the graph-theoretic properties of the digraph underlying the circuit. The analysis is based on a reformulation of independent interest of the saddle-node theorem of Sotomayor for semiexplicit index one differential-algebraic equations (DAEs), which define the natural context to set up nonlinear circuit models. The bifurcation is addressed not only for classical circuits, but also for circuits with memristors. The presence of this device systematically leads to nonisolated equilibria, and in this context the saddle-node bifurcation is shown to yield a bifurcation of manifolds of equilibria; in cases with a single memristor, this phenomenon describes the splitting of a line of equilibria into two, with different stability properties

Memristor circuits: bifurcations without parameters

The present manuscript relies on the companion paper entitled ''Memristor Circuits: Flux-Charge Analysis Method,'' which has introduced a comprehensive analysis method to study the nonlinear dynamics of memristor circuits in the flux-charge (φ,q)-domain. The Flux-Charge Analysis Method is based on Kirchhoff Flux and Charge Laws and constitutive relations of circuit elements in terms of incremental fluxes and incremental charges. The straightforward application of the method has previously provided a full portrait of the nonlinear dynamics and bifurcations of the simplest memristor circuit composed by a capacitor and a flux-controlled memristor. This paper aims to show that the method is effective to analyze nonlinear dynamics and bifurcations in memristor circuits with more complex dynamics including Hopf bifurcations (originating persistent oscillations) and period-doubling cascades (leading to chaotic behavior). One key feature of the method is that it makes clear how initial conditions give rise to bifurcations for an otherwise fixed set of circuit parameters. To the best of the authors' knowledge, these represent the first results that relate such bifurcations, which are referred to in the paper as Bifurcations without Parameters, with physical circuit variables as the initial conditions of dynamic circuit elements

Synchronization between two chaotic memristor circuits via the flux-charge analysis method

Recent articles introduced a new method, named flux-charge analysis method (FCAM), for studying nonlinear dynamics and bifurcations of a large class of memristor circuits. FCAM is based on Kirchhoff flux and charge Laws, and constitutive relations of basic circuits elements, expressed in the flux-charge domain. As such, FCAM is in contrast with other traditional methods for studying the dynamics of memristor circuits, that are instead based on the analysis in the standard voltage-current domain. So far, FCAM has been used to study saddle-node bifurcations of equilibrium points in the simplest memristor circuit composed of an ideal flux-controlled memristor and a capacitor, and more complex Hopf and period doubling bifurcations in certain classes of second- A nd third-order oscillatory memristor circuits. These bifurcations may be induced by varying initial conditions for a fixed set of circuit parameters (bifurcations without parameters). A peculiar property proved via FCAM is that the state space of a memristor circuit can be decomposed in infinitely many invariant manifolds, where each manifold is characterized by a different reduced-order dynamics and attractors. In this paper, FCAM is used for studying synchronization phenomena that can be observed in resistively-coupled arrays of chaotic memristor circuits. In particular, the paper considers two coupled memristor circuits such that each uncoupled circuit displays a double-scroll chaotic attractor on a certain invariant manifold. It is demonstrated via simulations how phase-synchronization of the two coupled attractors can be achieved depending on the choice of the coupling strength