On second-order differential equations with highly oscillatory forcing terms

We present a method to compute efficiently solutions of systems of ordinary differential equations that possess highly oscillatory forcing terms. This approach is based on asymptotic expansions in inverse powers of the oscillatory parameter,and features two fundamental advantages with respect to standard ODE solvers: rstly, the construction of the numerical solution is more efficient when the system is highly oscillatory, and secondly, the cost of the computation is essentially independent of the oscillatory parameter. Numerical examples are provided, motivated by problems in electronic engineering

Motion direction control of a robot based on chaotic synchronization phenomena

This work presents chaotic motion direction control of a robot and especially of a humanoid robot, in order to achieve complete coverage of the entire work terrain with unpredictable way. The method, which is used, is based on a chaotic true random bits generator. The coexistence of two different synchronization phenomena between mutually coupled identical nonlinear circuits, the well-known complete chaotic synchronization and the recently new proposed inverse π-lag synchronization, is the main feature of the proposed chaotic generator. Computer simulations confirm that the proposed method can obtain very satisfactory results in regard to the fast scan of the entire robot’s work terrain

Analysis, adaptive control and synchronization of a novel 4-D hyperchaotic hyperjerk system and its SPICE implementation

A hyperjerk system is a dynamical system, which is modelled by an nth order ordinary differential equation with n 4 describing the time evolution of a single scalar variable. Equivalently, using a chain of integrators, a hyperjerk system can be modelled as a system of n first order ordinary differential equations with n 4. In this research work, a 4-D novel hyperchaotic hyperjerk system has been proposed, and its qualitative properties have been detailed. The Lyapunov exponents of the novel hyperjerk system are obtained as L1 = 0:1448;L2 = 0:0328;L3 = 0 and L4 = −1:1294. The Kaplan-Yorke dimension of the novel hyperjerk system is obtained as DKY = 3:1573. Next, an adaptive backstepping controller is designed to stabilize the novel hyperjerk chaotic system with three unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve global hyperchaos synchronization of the identical novel hyperjerk systems with three unknown parameters. Finally, an electronic circuit realization of the novel jerk chaotic system using SPICE is presented in detail to confirm the feasibility of the theoretical hyperjerk model

Analysis, adaptive control and circuit simulation of a novel finance system with dissaving

In this paper a novel 3-D nonlinear finance chaotic system consisting of two nonlinearities with negative saving term, which is called ‘dissaving’ is presented. The dynamical analysis of the proposed system confirms its complex dynamic behavior, which is studied by using wellknown simulation tools of nonlinear theory, such as the bifurcation diagram, Lyapunov exponents and phase portraits. Also, some interesting phenomena related with nonlinear theory are observed, such as route to chaos through a period doubling sequence and crisis phenomena. In addition, an interesting scheme of adaptive control of finance system’s behavior is presented. Furthermore, the novel nonlinear finance system is emulated by an electronic circuit and its dynamical behavior is studied by using the electronic simulation package Cadence OrCAD in order to confirm the feasibility of the theoretical model

A chaotic path planning generator enhanced by a memory technique

This work considers the problem of chaotic path planning, using an improved memory technique to boost performance. In this application, the dynamics of two simple chaotic maps are first used to generate a pseudo-random bit generator. Using this as a source, a series of navigation commands are generated and used by an autonomous robot to explore an area, while maintaining a random and unpredictable motion. This navigation strategy can bring overall area coverage, but also yields numerous revisits to previous cells. Here, a memory technique is applied to limit the chaotic motion of the robot to adjacent cells with the least number of visits, leading to overall improvement in performance. Numerical simulations are performed to evaluate the path planning strategy. The simulation results showcase a major improvement in coverage performance compared to the memory-free technique and also compared to an inverse pheromone technique previously developed by the authors. Also, the number of multiple visits to previous cells is significantly reduced with the proposed technique. © 2021 Elsevier B.V

Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities

In this research work, a six-term 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities has been proposed, and its qualitative properties have been detailed. The Lyapunov exponents of the novel jerk system are obtained as L1 = 0.07765,L2 = 0, and L3 = −0.87912. The Kaplan-Yorke dimension of the novel jerk system is obtained as DKY = 2.08833. Next, an adaptive backstepping controller is designed to stabilize the novel jerk chaotic system with two unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve complete chaos synchronization of the identical novel jerk chaotic systems with two unknown parameters. Finally, an electronic circuit realization of the novel jerk chaotic system using Spice is presented in detail to confirm the feasibility of the theoretical model

Experimental Verification of Optimized Multiscroll Chaotic Oscillators Based on Irregular Saturated Functions

Multiscroll chaotic attractors generated by irregular saturated nonlinear functions with optimized positive Lyapunov exponent are designed and implemented. The saturated nonlinear functions are designed in an irregular way by modifying their parameters such as slopes, delays between slopes, and breakpoints. Then, the positive Lyapunov exponent is optimized using the differential evolution algorithm to obtain chaotic attractors with 2 to 5 scrolls. We observed that the resulting chaotic attractors present more complex dynamics when different patterns of irregular saturated nonlinear functions are considered. After that, the optimized chaotic oscillators are physically implemented with an analog discrete circuit to validate the use of proposed irregular saturated functions. Experimental results are consistent with MATLAB™ and SPICE circuit simulator. Finally, the synchronization between optimized and nonoptimized chaotic oscillators is demonstrated