Oscillations and stability of dynamics of hybrid biostructure

Hedrih, Andjelka; Hedrih, Katica

doi:10.1140/epjs/s11734-021-00240-8

Cited by 4 publications

(3 citation statements)

References 6 publications

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“…Therefore, it is possible to assume that all the conditions of Hopf bifurcation theory [20], [21] about the existence of limit cycles in the dynamic system (20) are fulfilled. From relation (22) we get:…”

Section: Methodsmentioning

confidence: 99%

“…Further theoretical studies have shown that dynamic systems of different nature have common features, for the definition of which it is appropriate to use the theory of bifurcations. Since then, system dynamics has become the subject of research by specialists in various fields of science, namely, in the field of mechanics and electromechanics [37], [41], in chemistry [40], in the field of economics [4], [10], [31], sociology [14], [19], biology and ecology [22], health care [39] and many others. The presence of bifurcations is inherent in most dynamic systems, and this should be considered the rule rather than the exception, so bifurcation analysis is very important for understanding the dynamic properties of complex systems.…”

Section: Literature Reviewmentioning

confidence: 99%

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Non-linear model of the macroeconomic system dynamics: multiplier-accelerator

Dorokhov,

Lebedeva,

Malyarets

et al. 2023

BUT_Series_III

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The article discusses one of the classic problems of macroeconomic dynamics, on which the neo-Keynesian theory of growth is based, so that the interaction between the multiplier and the accelerator. A new approach was proposed to develop a mathematical model of the dynamics of the mutual multiplier, which indicates the marginal propensity to save as a result of the GDP growth, and the accelerator, which reflects the growth of capital of the national income in the multiplier. The model is based on the hypothesis of non-linear dependence of the consumption on the amount of profit. This assumes that consumption growth is limited, i.e., a saturation effect occurs. In addition, the model took into account the delayed reaction of the accelerator to the influence of the multiplier. Under building the model, the considered processes were considered continuous in time. This made it possible to provide the mathematical model ”accelerator - multiplier” as a system of two differential equations of the first order. The application of the developed model to the analysis of the dynamic properties of the macroeconomic system makes it possible to evaluate the parameters at which the ”multiplier-accelerator” system enters a critical state. It has been proven that the conditions for the occurrence of self-oscillations depend on the critical value of the accelerator power. The presence of a two-fold limit cycle with corresponding ”soft” and ”hard” modes of birth (death) of the limit cycle was also founded. The applied usefulness of the model is that the choice of management decisions taking into account these results allow us preventing the occurrence of bifurcations and disasters in the process of evolution of the macroeconomic systems.

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Section: Methodsmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

Non-linear model of the macroeconomic system dynamics: multiplier-accelerator

Dorokhov,

Lebedeva,

Malyarets

et al. 2023

BUT_Series_III

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“…Hedrih [13] analyzes the free and forced oscillatory motions of a model of a hybrid biostructure and investigates their stability with respect to the geometrical and kinematic parameters of the model. The basic biostructure is modelled as a cantilever of circular cross-section with rigidly connected structures and discrete masses, and has three degrees of freedom.…”

Section: Contributed Papers In This Special Issuementioning

confidence: 99%

Mathematical modelling, nonlinear dynamics, bifurcation, synchronization and control of mechanisms driven by power supply

Balthazar

Gonçalves

Tusset

et al. 2021

Eur. Phys. J. Spec. Top.

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The special issue entitled "Mathematical modelling, nonlinear dynamics, bifurcation, synchronization and control of mechanisms driven by power supply," published by The European Physical Journal: Special Topics (EPJST), aims to bring into discussion works involving nonlinear and dynamic and chaotic behaviors, which are frequently found in mechanical and electromechanical systems, nonlinear circuits, and biologically inspired systems, stimulating the integration of findings on the nonlinear dynamics that can be observed in various systems in the physical sciences and engineering. This special issue presents 27 papers concerning the dynamics and control of flexible structure systems, nonideal systems, energy harvesting problems, and vibration absorbers. In addition, the papers address problems involving chaos control of nonlinear oscillations, phase-locked loops, synchronization of nonlinear oscillators, dynamics of bio-inspired and biostructural systems, nonlinear methods, and nonlinear circuits.

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Stability and Instability of a Complex Biodynamical Discrete Structure on a Cantilever Coupled to Nonlinear Springs

Hedrih,

Hedrih

2024

NODYCON Conference Proceedings Series

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Oscillations and stability of dynamics of hybrid biostructure

Cited by 4 publications

References 6 publications

Non-linear model of the macroeconomic system dynamics: multiplier-accelerator

Non-linear model of the macroeconomic system dynamics: multiplier-accelerator

Mathematical modelling, nonlinear dynamics, bifurcation, synchronization and control of mechanisms driven by power supply

Stability and Instability of a Complex Biodynamical Discrete Structure on a Cantilever Coupled to Nonlinear Springs

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