The global behavior of a quadratic difference equation

Hadžiabdić, Vahidin; Mehuljić, Midhat; Bektešević, Jasmin; Mujić, Naida

doi:10.2298/fil1818203h

Cited by 4 publications

(3 citation statements)

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“…The condition (2) of theorem 1 directly yields from (21). The passive output (22) was computed based on equation (3). • Since…”

Section: Passivity Of Lotka-volterra Systemsmentioning

confidence: 99%

“…Consider an open Lotka-Volterra system in which the state dynamics is defined by ( 17) and the output is given by (22).…”

Section: Feedback Equivalence Of Lotka-volterra Systems To Passive Systemsmentioning

confidence: 99%

“…The system with u c = w = 0 admits non-zero equilibrium points for all the three populations only if m 21 /l 2 = m 31 /l 3 , which is an eminently restrictive condition. Otherwise, one of the predator species dies out [22] and the dynamics of the system degenerates to a twodimensional Lotka-Volterra system, see example 1. However, using feedback control, the non-zero equilibrium for all the three species' populations can be assured.…”

Section: Lotka-volterra Modelmentioning

confidence: 99%

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Passivity of Lotka–Volterra and quasi-polynomial systems

2021

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This study approaches the stability analysis and controller design of Lotka–Volterra and quasi-polynomial systems from the perspective of passivity theory. The passivity based approach requires to extend the autonomous system model with a suitable input structure. The condition of passivity for Lotka–Volterra systems is less strict than the classic asymptotic stability criterion. It is shown that each Lotka–Volterra system is feedback equivalent to a passive system and a passifying state feedback controller is proposed. The passivity based approach enables the design of novel state feedback controllers to Lotka–Volterra systems. The asymptotic stability can be achieved by applying an additional diagonal state feedback having arbitrarily small gains. This result was further explored to achieve rate disturbance attenuation in controlled Lotka–Volterra systems. By exploiting the dynamical similarities between the Lotka–Volterra and quasi-polynomial systems, it was shown that the passivity related results, developed for Lotka–Volterra systems, are also valid for a large class of quasi-polynomial systems. The methods and tools developed have been illustrated through simulation case studies.

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“…The condition (2) of theorem 1 directly yields from (21). The passive output (22) was computed based on equation (3). • Since…”

Section: Passivity Of Lotka-volterra Systemsmentioning

confidence: 99%

“…Consider an open Lotka-Volterra system in which the state dynamics is defined by ( 17) and the output is given by (22).…”

Section: Feedback Equivalence Of Lotka-volterra Systems To Passive Systemsmentioning

confidence: 99%

Section: Lotka-volterra Modelmentioning

confidence: 99%

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