Analysis and Synchronization of a New Hyperchaotic System with Exponential Term

In this paper, a new four-dimensional hyperchaotic system with an exponential term is presented. The basic dynamical properties and chaotic behavior of the new attractor are analyzed. It can be shown that this system possesses either a line of equilibria or a single one. The existence of hyperchaos is confirmed by its Lyapunov exponents. Moreover, the synchronization problem for the hyperchaotic system is studied. Based on the Lyapunov stability theory, an adaptive control law with two inputs is proposed to achieve the global synchronization. Numerical simulations are given to validate the correctness of the proposed control law.

A Pneumatic Generator Based on Gas-Liquid Reversible Transition for Soft Robots

The soft robots actuated by pressure, cables, thermal, electrosorption, combustion and smart materials are usually faced with the problems of poor portability, noise, weak load capacity, small deformation and high driving voltages. In this paper, a novel pneumatic generator for soft robots based on the gas-liquid reversible transition is proposed, which has the advantages of large output force, easy deformation, strong load capacity and high flexibility. The pressure of the pneumatic generator surges or drops flexibly through the reversible transformation between liquid and gas phase, making the soft actuator stretch or contract regularly, without external motors, compressors and pressure-regulating components. The gas-liquid reversible-transition actuation process is modeled to analyze its working mechanism and characteristics. The pressure during the pressurization stage increases linearly with a rate regulated by the heating power and gas volume. It decreases exponentially with the exponential term as a quadratic function of time at the fast depressurization stage, while with the exponential term as a linear function of time at the slow depressurization stage. The drop rate can be adjusted by changing the gas volume and cooling conditions. Furthermore, effectiveness has been verified through experiments of the prototype. The pressure reaches 25 bar with a rising rate of +3.935 bar/s when 5 mL weak electrolyte solution is heated at 800 W, and the maximum depressurization rate in air cooling is –3.796 bar/s. The soft finger actuated by the pneumatic generator can bend with an angular displacement of 67.5°. The proposed pneumatic generator shows great potential to be used for the structure, driving and sensing integration of artificial muscles.

(p,Q) systems with critical singular exponential nonlinearities in the Heisenberg group

The paper deals with the existence of solutions for (p,Q) coupled elliptic systems in the Heisenberg group, with critical exponential growth at infinity and singular behavior at the origin. We derive existence of nonnegative solutions with both components nontrivial and different, that is solving an actual system, which does not reduce into an equation. The main features and novelties of the paper are the presence of a general coupled critical exponential term of the Trudinger-Moser type and the fact that the system is set in {{\mathbb{H}}}^{n} .