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Therapeutic agents acting on RNA, including RNA modification, RNA editing and RNA interference (RNAi), play a vital role in gene function study, signaling pathway, drug discovery, disease treatment, vaccine development and so on. Therein, RNAi as an emerging gene therapy has been widely applied in many cancer studies by silencing oncogenes or specific mRNA in malignant tumor cells. Mechanism and efficiency of RNAi are the key issues of RNAi technology. RNA silencing involves dynamic modeling, analyses and optimal control of RNAi gene system. Physiological delay and Hill response describing off-target are considerable elements involving RNAi efficiency. In this paper, we first formulate a four-dimensional RNAi model with time delays and Hill functions, and then investigate the complex dynamic behaviors including the number, existence and stability of internal equilibria and Hopf bifurcations of single delay and two delays. Furthermore, based on the specific mRNA degradation adopted in impulsive patterns, we build an optimal problem by adding exogenous dsRNA at alterable time points in variable dosages in a treatment session. By the method of gradient formula, we can find the optimal impulsive time and proportion of dsRNA. Finally, simulation indicates that (1) physiological lags not only raise the oscillations of mRNA but also cut down the levels of cost; (2) smaller delays and larger rates of siRNA–mRNA complex formation and dsRNA synthesis imply the rapid composition of RISC and fast synthesis of dsRNA leading to more desirable therapeutic schedule, which affords evidence for gene regulation and RNAi; (3) a larger half-saturation coefficient characterizes a unique and stable higher targeted mRNA, whereas a smaller half-saturation coefficient generates bistability in which the higher and lower targeted mRNAs simultaneously emerge; and (4) the bistability will provide a good guidance to control, suppress and degrade targeted mRNA. [ABSTRACT FROM AUTHOR]

This paper delves into the topics of Finite-Time Stabilization (FTS) and Finite-Time Contractive Stabilization (FTCS) for Fractional-Order Nonlinear Systems (FONSs). To address these issues, we employ a State-Dependent Delayed Impulsive Controller (SDDIC). By leveraging both Lyapunov theory and impulsive control theory, we establish sufficient conditions for achieving stability criteria for fractional-order systems. Initially, we employ the aforementioned sufficient conditions to derive stability criteria for general FONSs within the SDDIC framework, employing Linear Matrix Inequality (LMI) techniques. Furthermore, we apply these theoretical findings to tackle the challenge of finite-time synchronization in fractional-order chaotic systems using the proposed SDDIC. We substantiate the efficacy of these theoretical advancements through numerical simulations that vividly demonstrate their capability to achieve finite-time synchronization in fractional-order cellular neural networks and fractional-order Chua's circuits. Moreover, we introduce an innovative chaos-based multi-image encryption algorithm, thereby contributing significantly to the field. To ensure the algorithm's robustness, we subject it to rigorous statistical tests, which confidently affirm its capacity to provide the requisite level of security. [ABSTRACT FROM AUTHOR]

The investigation of new chaotic systems in spherical coordinates has been one of the present exciting research directions in exploring new chaotic systems. In this paper, a new system in spherical coordinates is presented. The appealing feature of the proposed system is that the dynamics of the system cannot pass through a sphere of a specific radius and stop as soon as the solution crosses the sphere in Cartesian coordinates. So, the system's attractors are limited to be located on one side of the sphere and cannot touch it. Moreover, the reason for this phenomenon is that the velocity of a system's variable becomes zero for a specific value of that variable. The proposed system has three unstable equilibrium points and four hidden attractors, including a limit cycle and a strange attractor inside and a limit cycle and a strange attractor outside the sphere. The system's dynamical properties are investigated with the help of bifurcation diagrams and the calculation of Lyapunov exponents. The basin of attraction for the system's attractors is also studied. Finally, the system is controlled or stabilized using the impulsive control theory. [ABSTRACT FROM AUTHOR]

This paper presents a new four-dimensional chaotic system with three nonlinearities and two equilibria. The most striking feature of the new system is that it has different types of asymmetric coexisting attractors. Simulation experiments are used to study the complex dynamic behaviors of the system. The chaos, period-doubling bifurcation, coexisting attractors with respect to system parameters and initial values are found in the system. It shows that the system has coexisting chaotic attractors, coexisting periodic attractors, coexisting chaotic and periodic attractors. The electronic circuit is applied to implement the chaotic attractor and coexisting attractors for studying the physical significance of the system. In addition, we consider the synchronization of the system by using the impulsive control method. Some synchronization criteria are established via theoretical analysis and simulation example. [ABSTRACT FROM AUTHOR]

An epidemic model for pest management with impulsive control over a patchy environment is proposed in this paper. We investigate the dynamical behaviors on extinction and permanence and obtain the threshold value R 0 of dynamics for the impulsive system by utilizing a small amplitude perturbation method, matrix spectral analysis and persistence theory. We prove that the periodic pest-eradication solution of the system is globally asymptotically stable if R 0 < 1 , while the system is persistent if R 0 > 1. Furthermore, by discussion on the two-patch case, we analyze the effects of the dispersal and impulsive control on dynamical behaviors of the system. Some numerical examples are given to illustrate the effectiveness of the obtained results and to demonstrate the complexity such as chaotic characteristic of the system. [ABSTRACT FROM AUTHOR]

In this paper, an impulsive Kolmogorov-type system using the Caputo fractional-order derivative is developed. The fractional-order system displays many interesting dynamic behaviors and fractional integrals can be used to describe the fractal media. The existence and stability of integral manifolds for the impulsive fractional model are considered. The main results are proved by means of piecewise continuous Lyapunov functions and the new fractional comparison principle. The impulses are realized at variable impulsive moments of time and can be considered as a control. Finally, an example is given to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, cluster synchronization in community network with nonidentical nodes is investigated. Through introducing proper adaptive strategy into impulsive control scheme, adaptive impulsive controllers are designed for achieving the cluster synchronization. In this adaptive impulsive control scheme, for any given networks, the impulsive gains can adjust themselves to proper values according to the proposed adaptive strategy when the impulsive intervals are fixed. The impulsive instants can be estimated by solving a sequence of maximum value problems when the impulsive gains are fixed. Both community networks without and with coupling delay are considered. Based on the Lyapunov function method and mathematical analysis technique, two synchronization criteria are derived. Several numerical examples are performed to verify the effectiveness of the derived theoretical results. [ABSTRACT FROM AUTHOR]

The field of bifurcation control includes several classes of problems that are actively studied with various motivations and from different points of view. The different statements of the problem are articulated by defining various objectives of applying control to the system, depending on the motivation and the specific problem. In this paper, we propose the objective of bifurcation control that is based on one of the main features of bifurcation phenomena: bifurcation generates possibilities for different scenarios to occur. We show how to find the right directions to control the system in order to ensure the realization of a favorable scenario. Our method is based on a bifurcation theorem for an abstract problem with constraints (inequalities). This theorem is further applied to controlled dynamical systems and two reasonably simple bifurcation control problems are analyzed in order to illustrate our objective and method. [ABSTRACT FROM AUTHOR]

The memristor is a novel nonlinear passive circuit element which has the memory function, and the circuits based on the memristors might exhibit chaotic behavior. In this paper, we revisit a memristor-based chaotic circuit, and then investigate its stabilization and synchronization via impulsive control. By impulsive system theory, some sufficient conditions for the stabilization and synchronization of the memristor-based chaotic system are established. Moreover, an estimation of the upper bound of the impulse interval is proposed under the condition that the parameters of the chaotic system and the impulsive control law are well defined. To show the effectiveness of the theoretical results, numerical simulations are also presented. [ABSTRACT FROM AUTHOR]

In this paper, we study the dynamical behavior of a prey-dependent digestive model with a state-dependent impulsive effect. Using the Poincaré map and the Lambert W-function, we find the analytical expression of discrete mapping. Sufficient conditions are established for transcritical bifurcation and period-doubling bifurcation through an analytical method. Exact locations of these bifurcations are explored. Numerical simulations of an example are illustrated which agree well with our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behavior of a Hamiltonian system under impulsive control is discussed by both theoretical and numerical analyses. The existence and stability of its period-one and period-three solutions are obtained in virtue of a discrete map. The conditions of existence for flip bifurcation and Hopf bifurcation are further derived by using center manifold theorem and bifurcation theory. Three attracting invariant closed curves, surrounding three fixed points respectively, are investigated. Moreover, chaos in the sense of Marotto is rigorously proven. Finally, some detailed numerical results including periodic solutions, bifurcation diagrams, and chaotic attractors, are illustrated by examples, which are in good agreement with the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we propose two impulsive differential systems concerning biological and, respectively, integrated pest management strategies. In each case, it is observed that there exists a globally asymptotically stable susceptible pest-eradication periodic solution on condition that the amount of infective pests released periodically is larger than a certain critical value. When the amount of infective pests released is less than this critical value, the system is shown to be permanent, which implies that the trivial susceptible pest-eradication solution loses its stability. Further, the existence of a non-trivial periodic solution is also studied by means of numerical simulations. In the case in which a single control is used, one can only use the amount of infective pests which are periodically released in order to control pests at desirable low levels, while in the case in which integrated management is used, one can use the proportion of pests removed by means of spraying chemical pesticides together with the amount of infective pests which are periodically released to control pests at desirable low levels. [ABSTRACT FROM AUTHOR]

In this paper, a new hybrid impulsive and switching control strategy for synchronization of nonlinear systems is developed. Using switched Lyapunov functions, several new criteria for global exponential stability of hybrid impulsive and switching nonlinear systems are established and, particularly, some simple sufficient conditions for driving the synchronization error to zero exponentially are proposed. As an application, Chua's chaotic circuit is investigated. [ABSTRACT FROM AUTHOR]

In this paper, the problem of chaotifying the continuous-time fuzzy hyperbolic model (FHM) is considered. We use impulsive and nonlinear feedback control methods to chaotify the FHM and show that chaos produced by the present methods satisfy the three criteria of Devaney. Computer simulations will be used to verify the present results. [ABSTRACT FROM AUTHOR]

This paper derives some sufficient conditions for the stabilization and synchronization of n-scroll attractors via impulsive control with varying impulsive intervals. Some sufficient conditions for the stabilization and synchronization of n-scroll attractors are obtained. The results are illustrated to be efficient through a numerical example and simulation results. [ABSTRACT FROM AUTHOR]

In this paper, a method that combines impulsive control and sporadic coupling for the synchronization of two Lorenz systems is proposed. The time required to synchronize the Lorenz systems can be readily computed. With this scheme, the Lorenz systems can be synchronized quickly and the time interval between successive impulsive signals can be made larger. This will improve the efficiency of channel bandwidth utilization when applied to secure communications. The results obtained in this paper are very useful in the applications of chaos-based secure communication systems. [ABSTRACT FROM AUTHOR]

This paper presents a time-delayed impulsive feedback approach to the problem of stabilization of periodic orbits in chaotic hybrid systems. The rigorous stability analysis of the proposed method is given. Using the time-delayed impulsive feedback method, we analyze the problem of detecting various periodic orbits in a special class of hybrid system, a switched arrival system, which is a prototype model of many manufacturing systems and computer systems where a large amount of work is processed in a unit time. We also consider the problem of stabilization of periodic orbits of chaotic piecewise affine systems, especially Chua's circuit, which is another important special class of hybrid systems. [ABSTRACT FROM AUTHOR]