OPEN- AND CLOSED-LOOP EQUILIBRIUM CONTROL OF TROPHIC CHAINS

If a nearly natural population system is deviated from its equilibrium, an important task of conservation ecology may be to control it back into equilibrium. In the paper a trophic chain is considered, and control systems are obtained by changing certain model parameters into control variables. For the equilibrium control two approaches are proposed. First, for a fixed time interval, local controllability into equilibrium is proved, and applying tools of optimal control, it is also shown how an appropriate open-loop control can be determined that actually controls the system into the equilibrium in given time. Another considered problem is to control the system to a new desired equilibrium. The problem is solved by the construction of a closed-loop control which asymptotically steers the trophic chain into this new equilibrium. In this way, actually, a controlled regime shift is realized

Inclusion properties of certain subclasses of analytic functions defined by generalized Salagean operator

Let $A$ denote the class of analytic functions with the normalization $f(0)=f^{\prime }(0)-1=0$ in the open unit disc U=\{z:\left\vert z\right\vert <1\}.  Set $$f_{\lambda }^{n}(z)=z+\sum_{k=2}^{\infty }[1+\lambda (k-1)]^{n}z^{k}\quad(n\in N_{0};\ \lambda \geq 0;\ z\in U),$$ and define $f_{\lambda ,\mu }^{n}$ in terms of the Hadamard product f_{\lambda }^{n}(z)\ast f_{\lambda ,\mu }^{n}=\frac{z}{(1-z)^{\mu }}\quad (\mu >0;\ z\in U). In this paper, we introduce several subclasses of analytic functions defined by means of the operator $I_{\lambda ,\mu }^{n}:A\longrightarrow A$, given by I_{\lambda ,\mu }^{n}f(z)=f_{\lambda ,\mu }^{n}(z)\ast f(z)\quad (f\in A;\ n\in N_{0;}\ \lambda \geq 0;\ \mu >0). Inclusion properties of these classes and the classes involving the generalized Libera integral operator are also considered

A study on certain class of harmonic functions of complex order associated with convolution

In this paper, we introduce a new class of harmonic functions of complex order associated with convolution. We also derive the coefficient inequality, distortion theorem, extreme points, convolution conditions and convex combination for this class

Subclass of harmonic univalent functions defined by Dziok-Srivastava operator

In this paper we introduce a new class of harmonic univalent functions defined by the Dziok-Srivastava operator. Coefficient estimates, extreme points, distortion bounds and convex combination for functions belonging to this class are obtained and also for a class preserving the integral operator

Univalent harmonic functions defined by Salagean integral operator with respect to symmetric points

In this paper, we define and investigate a subclass of univalent harmonic functions defined by Salagean integral operator with respect to symmetric points. We obtain coefficient conditions, extreme points, distortion bounds, convex combinations for this family of harmonic univalent functions

Differential sandwich theorems for p-valent functions associated with generalized multiplier transformations

In this paper, we obtain some applications of theory of differential subordination, superordination and sandwich results involving an operator

State monitoring of a population system in changing environment

For Lotka-Volterra population systems, a general model of state monitoring is presented. The model includes time-dependent environmental effects or direct human intervention (treatment) as control functions and, instead of the whole state vector, the densities of certain indicator species (distinguished or lumped together) are observed. Mathematical systems theory offers a sufficient condition for local observability in such systems. The latter means that, based on the above (dynamic) partial observation, the state of the population can be recovered, at least near equilibrium. The application of this sufficient condition is illustrated by three-species examples such as a one-predator two-prey system and a simple food chain

Inclusion properties of certain subclasses of analytic functions defined by generalized Salagean operator

Let $A$ denote the class of analytic functions with the normalization $f(0)=f^{\prime }(0)-1=0$ in the open unit disc U=\{z:\left\vert z\right\vert <1\}.  Set $$f_{\lambda }^{n}(z)=z+\sum_{k=2}^{\infty }[1+\lambda (k-1)]^{n}z^{k}\quad(n\in N_{0};\ \lambda \geq 0;\ z\in U),$$ and define $f_{\lambda ,\mu }^{n}$ in terms of the Hadamard product f_{\lambda }^{n}(z)\ast f_{\lambda ,\mu }^{n}=\frac{z}{(1-z)^{\mu }}\quad (\mu >0;\ z\in U). In this paper, we introduce several subclasses of analytic functions defined by means of the operator $I_{\lambda ,\mu }^{n}:A\longrightarrow A$, given by I_{\lambda ,\mu }^{n}f(z)=f_{\lambda ,\mu }^{n}(z)\ast f(z)\quad (f\in A;\ n\in N_{0;}\ \lambda \geq 0;\ \mu >0). Inclusion properties of these classes and the classes involving the generalized Libera integral operator are also considered

On Sandwich Theorem of Analytic Functions Involving Integral Operator

2000 Mathematics Subject Classification: 30C4

Certain Subclasses of p-Valent Meromorphic Functions Associated with a New Operator

We introduce two classes of p-valent meromorphic functions associated with a new operator and derive several interesting results for these classes