We discuss a novel approach to control bifurcations in nonlinear systems. The aim of bifurcation tailoring is to design an appropriate control law such that the controlled system has a desired bifurcation diagram. After describing two open-loop bifurcation tailoring techniques, this paper proposes two alternative modified bifurcation tailoring methods based on the use of the Newton-flow algorit...

In this paper, we investigate the dynamics of a completely inelastic ball on a vertically vibrated plate. We construct a computational model using various forcing waveforms for the plate and generate associated bifurcation diagrams. The forcing functions used are a superposition of two sine waves with an integer ratio of frequencies. We then observe experimentally some of the predictions made b...

This paper presents N binary hysteresis relaxation oscillators connected by the Intermittently Coupled Capacitors. The network exhibits various interesting synchronous phenomena. As a powerful analysis tool, we derive a hybrid return map which has one real and N binary states. Using this map, the stability of the periodic synchronization can be analyzed simply by the binary states: it is not ne...

The results in this paper show that the cubic vector fields ẋ = −y + M(x, y) − y(x + y), ẏ = x + N(x, y) + x(x + y), where M,N are quadratic homogeneous polynomials, having simultaneously a center at the origin and at infinity, have at least 61 and at most 68 topologically different phase portraits. To this end the reversible subfamily defined by M(x, y) = −γxy, N(x, y) = (γ − λ)x + αλy with α,...

This paper presents existence theories for several families of small-amplitude solitarywave solutions to the classical water-wave problem in the presence of surface tension and with an arbitrary distribution of vorticity. Moreover, the established local bifurcation diagram for irrotational solitary waves is shown to remain qualitatively unchanged for any choice of vorticity distribution. The hy...

R. L. da Silva 1, H. A. Albuquerque 1, R. M. Rubinger 2, A. G. de Oliveira 1, G. M. Ribeiro 1, and W. N. Rodrigues 1 1Departamento de Fı́sica, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, Caixa Postal 702, 30123-970, Belo Horizonte, MG, Brazil 2Departamento de Fı́sica e Quı́mica, Instituto de Ciências, Universidade Federal de Itajubá, Caixa Postal 50, 37500-903, Itajubá, MG,...

We prove the exact multiplicity of positive boundary blow-up solutions to a semilinear elliptic equation with bistable nonlinearity for the one-dimensional case. We use time-mapping techniques to determine the exact shape of the bifurcation diagram.

We show that incorporating spatial dispersal of individuals into a simple vaccination epidemic model may give rise to a model that exhibits rich dynamical behavior. Using an SIVS (susceptible – infected – vaccinated – susceptible) model as a basis, we describe the spread of an infectious disease in a population split into two regions. In each sub-population, both forward and backward bifurcatio...

The forced response curve is a graph showing the amplitude of the response of a periodically forced system as the forcing frequency is varied. Zhang and Golubitsky (SIADS, 10(4) (2011) 1272–1306) classified the existence and multiplicity of periodic responses to small amplitude periodic forcing of a system near a Hopf bifurcation point, where the forcing frequency, ωF , is close to the Hopf fre...

With amplitude modulated excitation, the effect on chaotic behavior of Φ-Rayleigh oscillator with three wells is investigated in this paper. The Melnikov theorem is used to detect the conditions for possible occurrence of chaos. The results show that the domain of the appearance of chaos is enlarged as both amplitudes of modulated and unmodulated forces increase. The effect of these two amplitu...