This paper introduces a novel 6D dynamic system derived from modified 3D Lorenz equations of the second type using state feedback control. While the original 3D equations are formally simpler than the classical Lorentz equations, they produce topologically more complex attractors with a two-winged butterfly structure. The proposed system contains the fewest terms compared to existing literature. These terms comprise two cross-product nonlinearities, two piecewise linear functions, six linear terms, and one constant. The new 6D hyperchaotic system exhibits a rich array of dynamic characteristics, including hidden attractors and dissipative behavior. A thorough dynamic analysis of this system was performed. In particular, bifurcation diagrams were constructed, Lyapunov exponents and dimensions were calculated, and multistability and offset boosting control were analyzed to understand the systems behavior further. An electronic circuit of the 6D hyperchaotic two-winged butterfly system was developed in the Multisim computer environment. The designed electronic circuit showed excellent agreement with the simulation results of the new 6D dynamic system. Synchronization of two identical 6D hyperchaotic systems was achieved using the active control method.

Purpose—This study aims to perform an in-depth analysis of double-diffusive natural convection (DDNC) in an irregularly shaped porous cavity. We investigate the convective heat transfer process induced by the lower wall treated as a heat source while the side walls of the enclosure are maintained at a lower temperature and concentration, and the remaining wall is adiabatic. Various factors, such as the Rayleigh number, Darcy effects, Hartmann number, Lewis number and effects of magnetic inclination are evaluated for their influence on flow dynamics and heat distribution. Design/methodology/approach—After validating the results, the FEM (finite element method) is used to simulate the flow pattern, temperature variations, and concentration by solving the nonlinear partial differential equations with the modified Rayleigh number (10⁴ ≤ Ra ≤ 10⁷), Darcy number (10⁻⁴ ≤ Da ≤ 10⁻¹), Lewis number $(0.1\le Le\le 10)$, and Hartmann number $\left(0\le Ha\le 40\right)$ as the dimensionless operating parameters. Findings—The finding shows that the patterns of convection and the shape of the isotherms within porous enclosures are notably affected by the angle of the applied magnetic field. This study enhances our understanding of how double-diffusive natural convection (DDNC) operates in these enclosures, which helps improve heating and cooling technologies in various engineering fields. Research limitations/implications—Numerical and experimental extensions of the present study make it possible to investigate differences in thermal performance as a result of various curvatures, orientations, boundary conditions, and the use of three-dimensional analysis and other working fluids. Practical implications—The geometry configurations used in this study have wide-ranging applications in engineering fields, such as in heat exchangers, crystallization, microelectronics, energy storage, mixing, food processing, and biomedical systems. Originality/value—This study shows how an inclined magnetic field affects double-diffusive natural convection (DDNC) within a porous system featuring an irregularly shaped cavity, considering various multiphysical conditions.

We consider mathematical model of genetic regulatory networks (GRN). This model consists of a nonlinear system of ordinary differential equations. The vector of solutions X(t) is interpreted as a current state of a network for a given value of time t: Evolution of a network and future states depend heavily on attractors of system of ODE. We discuss this issue for low dimensional networks and show how the results can be applied for the study of large size networks. Examples and visualizations are provided

We developed a mathematical model to simulate the dynamics of background synaptic noise in non-neuronal cells. By employing the stochastic Ornstein–Uhlenbeck process, we represented excitatory synaptic conductance and integrated it into a whole-cell model to generate spontaneous and evoke cellular electrical activities. This single-cell model encompasses numerous biophysically detailed ion channels, depicted by a set of ordinary differential equations in Hodgkin–Huxley and Markov formalisms. Consequently, this approach effectively induced irregular spontaneous depolarizations (SDs) and spontaneous action potentials (sAPs), resembling electrical activity observed in vitro. The input resistance decreased significantly, while the firing rate of spontaneous action potentials increased. Moreover, alterations in the ability to reach the action potential threshold were observed. Background synaptic activity can modify the input/output characteristics of non-neuronal excitatory cells. Hence, suppressing these baseline activities could aid in identifying new pharmaceutical targets for various clinical diseases.

This paper introduces a new 3D chaotic attractor in a gene regulatory network. The proposed model has eighteen parameters. Formulas for characteristic numbers of critical points for three-dimensional systems were considered. We show that the three equilibrium points of the new chaotic 3D system are unstable and deduce that the three-dimensional system exhibits chaotic behavior. The possible outcomes of this 3D model were compared with the results of the Chua circuit. The bifurcation structures of the proposed 3D system are investigated numerically, showing periodic solutions and chaotic solutions. Lyapunov exponents and Kaplan-Yorke dimension are calculated. For calculations, the Wolfram Mathematica is used.