Pachpatte inequalities on time scales.
Partial generalized synchronization theorems of differential and discrete systems
This paper presents two theorems for designing controllers to achieve directional partial generalized synchronization (PGS) of two independent (chaotic) differential equation systems or two independent (chaotic) discrete systems. Two numerical simulation examples are given to illustrate the effectiveness of the proposed theorems. It can be expected that these theorems provide new tools for understanding and studying PGS phenomena and information encryption.
Periodicity and stability in neutral nonlinear dynamic equations with functional delay on a time scale.
Permanence and global attractivity of a delayed discrete predator-prey system with general Holling-type functional response and feedback controls.
Permanence for a discrete model with feedback control and delay.
Permanence for a generalized discrete neural network system.
Perron-type criterion for linear difference equations with distributed delay.
Perturbation method for linear difference equations with small parameters.
Plus-operators in Krein spaces and dichotomous behavior of irreversible dynamical systems with discrete time
We study dichotomous behavior of solutions to a non-autonomous linear difference equation in a Hilbert space. The evolution operator of this equation is not continuously invertible and the corresponding unstable subspace is of infinite dimension in general. We formulate a condition ensuring the dichotomy in terms of a sequence of indefinite metrics in the Hilbert space. We also construct an example of a difference equation in which dichotomous behavior of solutions is not compatible with the signature...
Positive decreasing solutions of higher-order nonlinear difference equations.
Positive fixed point theorems arising from seeking steady states of neural networks
Biological systems are able to switch their neural systems into inhibitory states and it is therefore important to build mathematical models that can explain such phenomena. If we interpret such inhibitory modes as `positive' or `negative' steady states of neural networks, then we will need to find the corresponding fixed points. This paper shows positive fixed point theorems for a particular class of cellular neural networks whose neuron units are placed at the vertices of a regular polygon. The...
Positive periodic solutions of abstract difference equations.
Positive periodic solutions of functional discrete systems and population models.
Positive periodic solutions of nonlinear first-order functional difference equations.
Positive solutions and oscillation of higher order neutral difference equations
Positive solutions for a system of nonlinear boundary-value problems on time scales.
Positive solutions for nonlinear difference equations involving the -Laplacian with sign changing nonlinearity.
Positive solutions of a singular positone and semipositone boundary value problems for fourth-order difference equations.
Positive solutions of four-point boundary-value problems for four-order -Laplacian dynamic equations on time scales.
Positive solutions of nonlinear -point boundary-value problem for -Laplacian dynamic equations on time scales.