The performance of two widely used chaos synchronization approaches, active control and backstepping control, is investigated in this study. These two methods are projected to synchronize two chaotic systems (Master/Drive of Rucklidge Systems) that are identical but have different initial conditions. The paper’s significant feature is that based on error dynamics, controllers are designed using the appropriate variable and the time synchronization between master Rucklidge and drive Rucklidge systems using both methods. The control function of the active control method is designed on the proper selection of matrices. The chaotic behavior is controlled using a recursive backstepping design based on the Lyapunov stability theory with a validated Lyapunov function. The effectiveness of the controller in eradicating the chaotic behavior from the state trajectories is also revealed using numerical simulations with Matlab. The backstepping method is superior to the active control method for synchronization of the measured pair of systems, as it takes less time to synchronize while exhausting the first one than the second one with great performance, according to numerical simulation and graphical outcomes.

Inlet and outlet orifices in an actuation chamber are sources through which the supply and exhaust pressures pass during the actuation process in clutch systems. They are key ingredients in an actuation chamber and are very phenomenal in heavy-duty vehicle operation. It is these pressures that initiate linear or rotary motions in drive systems. The pressure actions are processed in an enclosure termed an actuation chamber. Oftentimes, the forces or pressures produced in an actuation chamber are unknown and immeasurable owing to a lack of precise instruments to accomplish them. This challenge can only be approached via an improvised technique that requires experimentation. This is precisely what this presentation is all about. The knowledge of these parameters is important in the study of the actuation process in electro-pneumatic clutch systems of heavy-duty vehicles. The study was done with a Mercedes Benz Actros Truck Model MP 2, 2031 Actuator chamber. An empirical and analytical approach was adopted. Meter rule, Venire Callipers and Mass Spring Balance were deployed for the experiments. Piston coil or spring, clutch distance in the actuator, the cross-sectional diameter of the actuator, and displacement in the free lengths of the coils among others were measured. The results of the experiments were analysed and used to determine the values of the supply (inlet) and exhaust (outlet) pressures which results stood at 9.61 bars and 11.299 bars, respectively.

This paper aims at treating a study on the order of every element for addition and multiplication composition in the higher order of groups for different algebraic structures as groups; order of a group and order of element of a group in real numbers. Here we discuss the higher order of groups in different types of order which will give us practical knowledge to see the applications of the addition and multiplication composition. If G is a finite group, n is a positive integer and a ⋴ G, then the order of the products na. When G is a finite group, every element must have finite order. However, the converse is false: there are infinite groups where each element has finite order. For example, in the group of all roots of unity in C× each element has finite order. Finally, we find out the order of every element of a group in different types of higher order of group.

This paper uses the concept of algorithmic efficiency to present a unified theory of intelligence. Intelligence is defined informally, formally, and computationally. We introduce the concept of dimensional complexity in algorithmic efficiency and deduce that an optimally efficient algorithm has zero time complexity, zero space complexity, and an infinite dimensional complexity. This algorithm is used to generate the number line.

The current study is based on the DEM computer simulation of three experimental test devices with different dimensions to determine the difference in the results of the formation of shear and repose angles that the particles experience when grouped under the action of the gravitational force. In this respect, the experimental test devices with different height, width, and depth were geometrically modeled with iron pellet particles using morphology and a granulometric variation from 6 mm to 9 mm of equivalent diameter in its spherical shape. Depending on the results obtained, a reliable size of the experimental test device will be available to obtain the necessary data for a correct adjustment of the calibration parameters for the DEM simulation of mining-metallurgical processes that use granulated material of iron pellet.

The article is considering the third kind of nonlinear Volterra-Stieltjes integral equations with the solution by Lavrentyev regularizing operator. A uniqueness theorem was proved, and a regularization parameter was chosen. This can be used in further development of the theory of the integral equations in non-standard problems, classes in the numerical solution of third kind Volterra-Stieltjes integral equations, and when solving specific problems that lead to equations of the third kind.

In order to deal with unmodeled dynamics in large vehicle systems, which have an ill condition of the state matrix, the use of model order reduction methods is a good approach. This article presents a new construction of the sliding mode controller for singularly perturbed systems. The controller design is based on a linear diagonal transformation of the singularly perturbed model. Furthermore, the use of a single sliding mode controller designed for the slow component of the diagonalized system is investigated. Simulation results indicate the performance improvement of the proposed controllers.

The observed dynamical property illustrates that state feedback control may stabilize invariant attractor to stable state in a simple version of hematopoietic stem cell model. The stability character of the positive steady state is analyzed by the computation of the rightmost characteristic roots in complex plane. Hopf bifurcation points are tracked as the roots curve crossing imaginary axis from the left half plane to the right half plane continuously. The bifurcation direction and stability of the bifurcating periodical solution are discussed by norm form computation combined with the center manifold theory. Furthermore, the numerical simulation verifies that instead of chaos, system is stabilized to period-1, 2, 3, 4 and period-7 periodical solutions in some delay windows, and the continuous of periodical solutions is also numerical simulated with varying free parameters continuously.

The infinite dimensional partial delay differential equation is set forth and delay difference state feedback control is considered to describe the cell cycle growth in eukaryotic cell cycles. Hopf bifurcation occurs as varying free parameters and time delay continuously and the multi-layer oscillation phenomena of the homogeneous steady state of a simple gene-protein network module is investigated. Normal form is derived based on normal formal analysis technique combined with center manifold theory, which is further to compute the bifurcating direction and the stability of bifurcation periodical solutions underlying Hopf bifurcation. Finally, the numerical simulation oscillation phenomena is in coincidence with the theoretical analysis results.

The HIV problem is studied by version of delay mathematical models which consider the apoptosis of uninfected CD4+ T cells which cultured with infected T cells in big volume. The opportunistic infection and the apoptosis of uninfected CD4+ T cells are caused directly or indirectly by a toxic substance produced from HIV genes. Ubiquitously, the nonlinear incidence rate brings forth the increasing number of infected CD4+ T cells with introduction of small time delay, and in addition, there also exists a natural time delay factor during the process of virus replication. With state feedback control of time delay, the bifurcating periodical oscillating phenomena is induced via Hopf bifurcation. Mathematically, with the geometrical criterion applied in the stability analysis of delay model, the critical threshold of Hopf bifurcation in multiple delay differential equations which satisfy the transversal condition is derived. By applying reduction dimensional method combined with the center manifold theory, the stability of the bifurcating periodical solution is analyzed by the perturbation near Hopf point.