Spatiotemporal Dynamics in a Predator–Prey Model with Functional Response Increasing in Both Predator and Prey Densities

In this paper, a diffusive predator–prey system with a functional response that increases in both predator and prey densities is considered. By analyzing the characteristic roots of the partial differential equation system, the Turing instability and Hopf bifurcation are studied. In order to consider the dynamics of the model where the Turing bifurcation curve and the Hopf bifurcation curve intersect, we chose the diffusion coefficients d1 and β as bifurcating parameters. In particular, the normal form of Turing–Hopf bifurcation was calculated so that we could obtain the phase diagram. For parameters in each region of the phase diagram, there are different types of solutions, and their dynamic properties are extremely rich. In this study, we have used some numerical simulations in order to confirm these ideas.

Diagnostic of Tomato Nematode in Daloa (Côte d’Ivoire)

Symptomatological studies were carried out in two tomato growing areas in Daloa to estimate and identify the associated nematode populations. Symptoms were assessed by visual observation. The soil and root nematodes were extracted by Bermann's method and identified by observing morphological characteristics. The symptomatological study showed the presence of symptoms of plants wilting, yellowing of the leaves as well as galls on the nematodes characteristic roots. The results also highlighted diversity within the nematode population that colonizes tomato in Daloa with four genera of nematodes. The genera Tylenchus, Helicotylenchus, Partylenchus and Meloidogyne were identified. The presence of the genus Meloidogyne in all plots shows that it is responsible for the yellowing symptoms associated with root galls. These nematodes are known for their action on the formation of galls on the roots of the tomato.

Receptance-Based Computation of Stability Crossing Curves for Single-Input-Multiple-Output Second-Order Linear Systems with Two Time-Delays

For a complete stability analysis of multi-dimensional controlled systems modeled in the framework of second-order linear differential equations with two time-delays, the determination of stability crossing curves (or stability switching curves) within the domain of the delays is significantly important. This paper presents a simple receptance-based approach to solve this problem for a single-input-multiple-output controlled system using its second-order model. The proposed approach is based on a reduced characteristic function of the controlled system. This characteristic function is directly related to the receptance of the uncontrolled system and has a peculiar form that is well-suited for an effective method of calculation of these curves. Moreover, this method can find the direction in which the characteristic roots cross the imaginary axis as the delays deviate from a stability crossing curve. An example case study with two independent and constant delays is given to demonstrate the effectiveness of the proposed approach.

A simulation study of nonideal mixing effect on the dynamic response of an exothermic CSTR with Cholette’s model

The study of nonideal mixing effect on the dynamic behaviors of CSTRs has very rarely been published in the literature. In this work, Cholette’s model is employed to explore the nonideal mixing effect on the dynamic response of a nonisothermal CSTR. The analysis shows that the mixing parameter n (the fraction of the feed entering the zone of perfect mixing) and m (the fraction of the total volume of the reactor), indeed affect the characteristic roots of transfer function of a real CSTR, which determine the system stability. On the other hand, the inverse response and overshoot response are also affected by the nonideal mixing in a nonisothemal CSTR. These results are of much help for the design and control of a real CSTR.

Oriented by Characteristic Roots Reduced Matrices in the Class of Semiscalarly Equivalent

A set of polynomial 3 × 3 -matrices of simple structure has been singled out, for which a so-called oriented by certain characteristic roots reduced matrix is established in the class of semiscalarly equivalent. The invariants of such reduced matrices and the conditions of their semiscalar equivalence are indicated. The obtained results will also be applied to the problem of similarity of sets of numerical matrices.

A STUDY ABOUT STABILITY OF TWO AND THREE SPECIES POPULATION MODELS

In this article, we have discussed the stability of second order linear and non-linear systems by characteristic roots. In the case of non-linear system, we linearize the nonlinear system under certain specified conditions and study the stability of critical points of the linearized systems. Necessary theories have been presented, applied, and illustrated with examples. A self-contained theory for a homogeneous linear system of third order is built by using the basic concept of the differential equation.

Fast Generation of Stability Charts for Time-Delay Systems Using Continuation of Characteristic Roots

Many dynamic processes involve time delays, thus their dynamics are governed by delay differential equations (DDEs). Studying the stability of dynamic systems is critical, but analyzing the stability of time-delay systems is challenging because DDEs are infinite-dimensional. We propose a new approach to quickly generate stability charts for DDEs using continuation of characteristic roots (CCR). In our CCR method, the roots of the characteristic equation of a DDE are written as implicit functions of the parameters of interest, and the continuation equations are derived in the form of ordinary differential equations (ODEs). Numerical continuation is then employed to determine the characteristic roots at all points in a parametric space; the stability of the original DDE can then be easily determined. A key advantage of the proposed method is that a system of linearly independent ODEs is solved rather than the typical strategy of solving a large eigenvalue problem at each grid point in the domain. Thus, the CCR method can significantly reduce the computational effort required to determine the stability of DDEs. As we demonstrate with several examples, the CCR method generates highly accurate stability charts, and does so up to 10 times faster than the Galerkin approximation method.