The steady state and dynamic behavior of two-phase systems in physical equilibrium is investigated. The autonomous and non-autonomous systems are considered. The pseudo-arclength bifurcation technique reveals steady state multiplicity patterns not previously observed, including isola and mushroom patterns. It is shown that degenerate singular points of codimension 2, which violate the non-singu...

A new class of critical points, termed as perpetual points, where acceleration becomes zero but the velocity remains non-zero, are observed in dynamical systems. The velocity at these points is either maximum or minimum or of inflection behavior. These points also show the bifurcation behavior as parameters of the system vary. These perpetual points are useful for locating the hidden oscillatin...

We consider systems φ̇ = f(φ, λ) where f : R×R → R. Such systems often arise from space discretizations of parabolic PDEs. We are interested in branches (with respect to λ) of periodic solutions of such systems. In the present paper we describe a numerical continuation method for tracing such branches. Our methods are matrix-free, i.e., Jacobians are only implemented as actions, this enables us ...

In this paper we study the existence of critical points for noncoercive functionals, whose principal part has a degenerate coerciveness. A bifurcation result at zero for the associated differential operator is established.

Abstract Dynamical properties of limit cycles for a tropically discretized negative feedback model are numerically investigated. This has controlling parameter τ, which corresponds to time interval the evolution phase in cycles. By considering τ as bifurcation parameter, we find that ultradiscrete state emerges due lock caused by saddle-node bifurcation. Furthermore, focusing on max-plus model,...

the modeling investigation in this paper discusses the system level effects of a toxicant on a three species food chain system. in the models, we have assumed that the presence of top predator reduces the predatory ability of the intermediate predator. the stability analysis of the models is carried out and the sufficient conditions for the existence and extinction of the populations under the ...

We demonstrate by an example that the search for valley-ridge transition (VRT) points used in the commented paper does not always indicate a bifurcation of a reaction path. This was claimed.