Limit Cycle Bifurcations in a Class of Piecewise Smooth Polynomial Systems

In this paper, we consider the bifurcation problem of limit cycles for a class of piecewise smooth cubic systems separated by the straight line [Formula: see text]. Using the first order Melnikov function, we prove that at least [Formula: see text] limit cycles can bifurcate from an isochronous cubic center at the origin under perturbations of piecewise polynomials of degree [Formula: see text]. Further, the maximum number of limit cycles bifurcating from the center of the unperturbed system is at least [Formula: see text] if the origin is the unique singular point under perturbations.

On Some Reversible Cubic Systems

We study three systems from the classification of cubic reversible systems given by Żoła̧dek in 1994. Using affine transformations and elimination algorithms from these three families the six components of the center variety are derived and limit-cycle bifurcations in neighborhoods of the components are investigated. The invariance of the systems with respect to the generalized involutions introduced by Bastos, Buzzi and Torregrosa in 2021 is discussed. Computations are performed using the computer algebra systems Mathematica and Singular.

Analisis Dinamika Molekuler Pengaruh Suhu Tubuh Terhadap Keseimbangan Volume Human Serum Albumin (HSA) Menggunakan Model Potensial Lennard-Jones

Research on molecular dynamics analysis of the influence of body temperature on HSA fluid volume balance using the Lennard-Jones potential model with temperature variations of 35 ℃, 37 ℃, and 40 ℃ in the form of cubic systems in GROMACS applications. The results show that the denaturation of HSA that is affected by body temperature causes changes in osmotic pressure in the body with changes in the balance of HSA fluid volume. At temperatures of 35 ℃ denaturations occurs Thr566 to Gln580 with a distance of 20.9 A, Lys444 to Met446 with a distance of 5.76 A, Asn61 to Cys62 with a distance of 3.9 A, Glu570 to Ser579 with a distance of 18.09 A, and Gly431 to Cys438 with a distance of 11.43 A. At a temperature of 37 ℃ denaturations occurs Ile513 to Cys514 has a distance of 3.75 A, Pro303 to Glu311 has a distance of 12.78 A, Asn267 to Ser270 has a distance of 4.65 A, Leu275 to Cys279 has a distance of 7 A At a temperature of 40 ℃ denaturations occurs Ser304 to Glu311 with a distance of 11.38 A, Asn267 to Ile271 with a distance of 7.75 A, Asn61 to Cys62 with a distance of 3.9 A, and Ala511 to Cys514 with a distance of 4.86 A. RMSD results shows that stable structural changes occur in HSA with values of 2.6–9.0 nm. And the Lennard-Jones average energy yield shows that the interaction behavior between HSA atoms is dynamic. At a temperature of 35 ℃ of 7.97E + 05 kJ/mol, a temperature of 37 ℃ of 6.78 kJ/mol, and a temperature of 40 ℃ of 7.89E + 05 kJ/mol.