Proportional Feedback Method Research Articles

Intervention Time in Target-Oriented Chaos Control

The timing of interventions plays a central role in managing and exploiting biological populations. However, few studies in the literature have addressed its effect on population stability. The Seno equation is a discrete-time equation that describes the dynamics of single-species populations harvested according to the proportional feedback method at any moment between two consecutive censuses. Here we study a discrete-time equation that generalizes the Seno equation by considering the management and exploitation of populations through the target-oriented chaos control method. We investigate the combined effect of timing, targeting, and control on population stability, focusing on global stability. We prove that high enough control values create a positive equilibrium that attracts all positive solutions. We also prove that it is possible to determine parameter values to stabilize the controlled populations at any preset population size. Finally, we investigate the parameter combinations for which the management and exploitation are optimized in different scenarios.

Stabilization with target oriented control for higher order difference equations

Abstract For a physical or biological model whose dynamics is described by a higher order difference equation u n + 1 = f ( u n , u n − 1 , … , u n − k + 1 ) , we propose a version of a target oriented control u n + 1 = c T + ( 1 − c ) f ( u n , u n − 1 , … , u n − k + 1 ) , with T ≥ 0 , c ∈ [ 0 , 1 ) . In ecological systems, the method incorporates harvesting and recruitment and for a wide class of f, allows to stabilize (locally or globally) a fixed point of f. If a point which is not a fixed point of f has to be stabilized, the target oriented control is an appropriate method for achieving this goal. As a particular case, we consider pest control applied to pest populations with delayed density-dependence. This corresponds to a proportional feedback method, which includes harvesting only, for higher order equations.

Global stabilization of periodic orbits using a proportional feedback control with pulses

We investigate the stabilization of periodic orbits of one-dimensional discrete maps by using a proportional feedback method applied in the form of pulses. We determine a range of the parameter μ values representing the strength of the feedback for which all positive solutions of the controlled equation converge to a periodic orbit.

How to control chaotic behaviour and population size with proportional feedback

We study the control of chaos in one-dimensional discrete maps as they often occur in modelling population dynamics. For managing the population, we seek to suppress any possible chaotic behavior, leading the system to a stable equilibrium. In this Letter, we make a rigorous analysis of the proportional feedback method under certain conditions fulfilled by a wide family of maps. We show that it is possible to stabilize the chaotic dynamics towards a globally stable positive equilibrium, that can be chosen among a broad range of possible values. In particular, the size of the population can be enhanced by control in form of population reduction. This paradoxical phenomenon is known as the hydra effect, and it has important implications in the design of strategies in such areas as fishing, pest management, and conservation biology.

Maintenance of transient chaos using a neural-network-assisted feedback control.

A stable period-3 orbit in the parametric vicinity of a chaotic attractor is destabilized using two distinct feedback strategies. This results in the inception and subsequent maintenance of the otherwise short-lived chaotic transients. Both the techniques employed are based on the exclusion of trajectories from the near vicinity of the open loop stable period-3 attractor; the first relies on the traditional proportional feedback method while the second one includes a predictive term enabling delimitation of exclusion zones for the system dynamics. The implementation of these strategies involves construction of appropriate reference models in the form of an artificial-neural-network approximator.

Control of product selectivity for a model with mutating autocatalysis

The variation of the selectivity, defined as the yield of one reaction product divided by the total product yield, with the residence time in a model scheme based on “mutating autocatalysis” is considered. Operating conditions spanning several types of bifurcation are investigated and the selectivity observed from time-dependent integrations compared to those appropriate to steady-state operation. In one case, complex periodic solutions may develop through a period-doubling bifurcation sequence, leading to chaotic states. The simple proportional feedback method is used to compare the selectivity of different stabilised periodic orbit under these conditions. It is found that these different states all have similar selectivities to that observed in the autonomous chaotic state, but that a significant change in selectivity can be achieved at the same operating conditions by targeting a coexisting stable period-1 orbit lying on a separate branch of solutions.

Control of chaotic solutions of the Hindmarsh–Rose equations

Irregular bursting and spiking solutions of the Hindmarsh–Rose model for the electrical activity of neuron cell bodies have been converted by a chaos control algorithm to periodic spike trains. A proportional feedback method is used to control both chaotic spike trains and chaotic bursting by applying controlling perturbations to membrane parameters.

Efficient strategy for the occasionally proportional feedback method in controlling chaos.

In this work, the generic mechanism of the occasionally proportional feedback (OPF) technique in controlling chaos has been explored extensively. Except for stabilizing the unstable states that are embedded in the chaotic attractors, the OPF method is also found to generate a great number of new states during the control processes. The forms and characteristics of these new states have been addressed. Moreover, we clarify the roles of the parameters in the OPF method and this clarification leads to a practical and systematic approach in adjusting the parameters for control. To demonstrate the validity, an analogous electronic circuit of the resistively shunted Josephson junction oscillator is employed in addition to a numerical illustration of the logistic mapping.

Control and suppression of chaos in flared laser systems: a numerical analysis

Numerical analysis of control and suppression of chaos in flared laser systems is presented. In order to stabilize the chaotic output of such systems, both the periodic perturbation method and the proportional feedback method are examined with good results. Several variations of the proportional feedback method are presented. A certain rule of thumb for tuning the different control algorithms is demonstrated to be fruitful.

Keeping chaos at bay

The use of electronic circuits in studying chaotic dynamics and control are reviewed. Since all chaotic systems have several properties in common, simple circuits are analogous to much more complicated ones, such as lasers. Consequently, the methods developed to control chaos in electronic circuits are applicable to many diverse physical systems. The controlling device itself is a high-speed analog circuit. In applying perturbations, no calculations are made; instead, trial-and-error adjustments are used to locate the desired behavior. The initial observations of chaos in electronics, the development of the Ott-Grebogi-Yorke method for calculating the perturbations needed to stabilize a periodic orbit in a chaotic system and the occasional proportional feedback method, and their applications are discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>