In this paper, we study the cubic three-parameter autonomous planar system ẋ1 = k1 + k2x1 − x1 − x2, ẋ2 = k3x1 − x2, where k2, k3 > 0. Our goal is to obtain a bifurcation diagram; i.e., to divide the parameter space into regions within which the system has topologically equivalent phase portraits and to describe how these portraits are transformed at the bifurcation boundaries. Results may be a...

We continue the study of the structural stability and the bifurcations of planar bimodal linear dynamical systems (BLDS) (that is, systems consisting of two linear dynamics acting on each side of a straight line, assuming continuity along the separating line). Here, we enlarge the study of the bifurcation diagram of saddle/spiral BLDS to saddle/source BLDS and in particular we study the positio...

The nonlinear dynamics such as bifurcation and chaos has got lot of attention in research fraternity. The power electronics is a dynamic and nonlinear field in which chaos plays an important role. The time dynamic and nonlinearity is cannot be neglected or it is default case in power electronics. The present paper discusses the simulative study of Bifurcation and chaotic behaviour in the single...

The FitzHugh-Nagumo equation has been investigated with a wide array of different methods in the last three decades. Recently a version of the equations with an applied current was analyzed by Champneys, Kirk, Knobloch, Oldeman and Sneyd [5] using numerical continuation methods. They obtained a complicated bifurcation diagram in parameter space featuring a C-shaped curve of homoclinic bifurcati...

two-layer metallic sheets have wide applications in aerospace, marine, automotive and domestic industries due to their superlative characteristics. in this paper, the formability of two-layer sheet is investigated through analytical, experimental and numerical approaches. an analytical model is developed based on marciniak-kuczynski method associated hill’s non-quadratic yield criterion. formin...

Consider nonlinear dynamical systems modelled by parameterised differential and difference equations. When the values of the system parameters vary from those at which the system is currently operated, it can exhibit qualitative changes in behaviour and a steady-state may disappear or become unstable through a bifurcation [1, 2]. Bifurcation analysis is clearly useful and a bifurcation diagram ...

The bifurcation structure of a constraint Duffing van der Pol oscillator with a diode is analyzed and an objective bifurcation diagram is illustrated in detail in this work. An idealized case, where the diode is assumed to operate as a switch, is considered.In this case, the Poincaré map is constructed as a one dimensional map: a circle map. The parameter boundary between a torusgenerating regi...

We demonstrate unprecedented agreement between a theoretical two-dimensional bifurcation diagram and the corresponding experimental stability map of an optically injected semiconductor laser over a large range of relevant injection parameter values. The bifurcation diagram encompasses both local and global bifurcations mapping out regions of regular, chaotic, and multistable behavior in conside...

The bifurcation diagram is an iconic image of iterative real dynamics. It's structure can be illuminated using a family of polynomial curves, called critical curves. We can also apply these polynomials to pinpoint the locations of periodic components in the Mandelbrot set, the complex analog of the bifurcation diagram. Note: To reduce the size of the file, the graphics in this file have all bee...